CHANCE News 5.03

(4 Feb. 1996 to 27 Feb. 1996)


Prepared by J. Laurie Snell, with help from William Peterson, Fuxing Hou, Ma.Katrina Munoz Dy, and Joan Snell, as part of the CHANCE Course Project supported by the National Science Foundation.

Please send comments and suggestions for articles to

Back issues of Chance News and other materials for teaching a CHANCE course are available from the Chance web site:


What is chance but the rude stone which receives its life from the sculptor's hand?
Providence gives us chance--and man must mold it to his own designs.

Schiller, Don Carlos



Note: There was still a little mystery about who really was responsible for the remark that one person moving from state A to state B could raise the average IQ in both. Herb Caen, well known columnist for the San Francisco Chronicle, responded to an e-mail query verifying that he was the source of the remark.

Comments on the last chance news from our readers.

Regarding our reference to Marilyn, Sandy McGrae writes:


While I am quite prepared to believe that Marilyn is female, I am 99.9% confident that I am a 6 ft (Scottish) male. I don't know about Laurie!

Sandy has provided us a graceful way to inform our readers that Laurie is a male.

Bob Hayden sent the following comments relating to the "New Yorker" article on the inevitability of technological failures.

When CDs replaced LPs, the motto was "perfect sound forever". In general, proponents of a new technology tend to predict lower failure rates for the new technology based on the fact that the new is not subject to the failure modes of the old. Of course, it is subject to new failure modes, many of which are not known when the technology is introduced. I have thousands of LPs and hundreds of CDs and find that CDs are less likely to fail but when they do fail the CD is completely unplayable rather than just noisy or scratchy like an old LP.

In a similar vein, does aspirin have more and worse side effects than newer (and more expensive) drugs, or just better documented side effects because it's been around for so long?


Can you give other examples of the phenomenon described by Bob Hayden?

Regarding our references to the average number of murders per year in New York and the average temperature in a year, Paul Gunty writes:

Is it more realistic to figure an "average" for each season or each month than the entire year? As you know average is a tricky thing and certainly more murders are committed at different times of the year. While weather, I am sure is a factor, how does one figure that into the problem?

In fact I heard on the news recently that the FBI was able to capture a few more of the most wanted criminals because of the blizzard conditions. The report stated that in "bad weather, everyone just wants to go home and be safe."

Gunty also remarked that in a recent popular magazine, under its "facts and figures", gave the average temperature of Russia as 22.46 degrees, of Canada as 24.08 and of the United States as 52.5. He asks:

How does one calculate an "average temperature" for a country? Does the average for the United States include both Alaska and Hawaii, two big extremes?

What good is knowing the average temperature for a country the size of the Soviet Union, Canada, or the United States, each of which spans so many degrees of latitude?


How would you answer Gunty's questions?

Research links writing style to the risk of Alzheimer's.
The New York Times, 21 Feb. 1996, A12
Gina Kolata

Researchers from the University of Kentucky designed a study to see if education and an active mind protected against Alzheimer's disease. They studied 93 nuns born before 1917 who lived together in the same environment for 60 years. Now in their 80's, nearly a third have developed Alzheimer's disease, consistent with the general population. Fourteen have died and autopsies were carried out on their brains to look for marks of Alzheimer's disease.

The researchers were surprised to find that education appeared to offer no protection against Alzheimer's disease. However they did find something even more surprising.

Four years after the nuns entered the convent, and before they took their vows to permanently join the convent they were asked to write brief autobiographies. The researchers examined these and found that the nuns whose sentences were grammatically complex and full of ideas had sharp minds right up to their 80's while most of those whose sentences were simple and without complex grammatical constructions were demented by their 80's. They found that the writing characteristics observed when the nuns were 20 continued throughout their lives.

The researchers' finding if confirmed would suggest that Alzheimer's disease is a lifelong disease that just progresses very slowly. This is consistent with a German study that concluded that pathological changes in the brains, characteristic of Alzheimer's disease, could be traced about 50 years back and may even extend into adolescence.

Experts in Alzheimer's disease called the study surprising and elegant and called for further studies to try to see if these results could be replicated and explained.


(1) How would you characterize your writing?

(2) The article states:

In the nuns study, one rater analyzed the autobiographies, without knowing whether the nuns who wrote them had developed Alsheimer's disease, and a second rater independently checked 10 of them. The two raters concurred nearly 90% of the time.

What do you think "nearly 90% of the time means with 10 checks?
Why do you think the second rater only checked 10?

(3) Presumably, the writing hypothesis was not one that the researchers planned to test in their original design of the experiment. Should we be concerned about this?

Professors Chatterjee, Handcock, and Simonoff sent us the following article, including the abstract and a discussion of the way they used this example in their classes.

Time trouble for geyser: It's no longer Old Faithful.
The New York Times, 5 Feb. 1996, D1
James Brooke

Rick Hutchison, Yellowstone National Park's research geologist, reported that Old Faithful, the park's leading tourist attraction, has been slowing down. In 1950, the average time interval between eruptions was 62 minutes, in 1970 it was 66 minutes, and today it is 77 minutes. It is also apparently becoming more difficult to predict the time until the next eruption, with forecasts now being to within plus or minus ten minutes.

The changes of recent years seem to be produced by seismic activity. Scientists theorize that earthquakes can have two effects on geysers, either speeding up or slowing down the rate of supply of water. Quakes can either shake loose debris that clog rock channels that feed water to a geyser, resulting in more water and steam, or can crack open new underground channels, redirecting water to other geysers or hot springs. It is speculated that the latter process is affecting Old Faithful.

Comments from Samprit Chatterjee, Mark Handcock and Jeffrey Simonoff:

The Old Faithful geyser is a wonderful national icon, and is also a wonderful source of interesting data, due to its non-faithful faithful appearance. What do we mean by "non-faithful"? It is well-known that the time interval between eruptions of the geyser is not faithful at all (in the sense of being around one value consistently), as it has a bimodal distribution. About one-third of the time the time between eruptions is roughly 55 minutes, while about two-thirds of the time it is roughly 80 minutes. Unfortunately, the description in the article of average time intervals in different years gives the mistaken impression of a unimodal distribution.

We have used Old Faithful eruption data (circa 1978, 1979 and 1985) in our introductory classes for many years, and made a case based on these data the lead case in our book "A Casebook for a First Course in Statistics and Data Analysis" (Wiley, 1995), since students are often very surprised to find out just how faithful (or non-faithful) Old Faithful is. The specific characterization of the bimodal distribution mentioned in the previous paragraph comes from those data. The case also points out that a simple way to predict the time interval until the next eruption is to check whether the duration of the previous eruption was short (less than 3 minutes) or long (more than 3 minutes), and predict accordingly (55 minutes until the next eruption, or 80 minutes, respectively). This rule, derived using the 1978/1979 data, correctly predicts the 1985 values to within plus or minus 10 minutes about 90% of the time, right in line with what the Times article states.

The bimodality has a direct effect on the question of lengthening average time intervals between eruptions. There are two obvious ways that the average time interval could increase, without changing the basic underlying pattern of eruptions: by a general shift upwards of the entire distribution, or by a change in the probabilities of a short time interval versus a longtime interval (with long intervals becoming more probable). Presumably these two different possibilities would have different implications from a geothermal point of view, so it would be interesting to see if either possibility (or what other possibility) describes the observed lengthening of the average time interval.

We discovered that Richard Morin has his own Chance News in the form of a column in the Sunday "Washington Post" where he comments on interesting studies from the social sciences. In his most recent column he discusses four such studies.

UNCONVENTIONAL WISDOM. New facts and hot stats from the social sciences.
Washington Post, 25 Feb. 1996, C9
Richard Morin

The first study discussed was reported in the latest issue of the journal "Ethnology and Sociobiology". Two psychologists from the University of Vienna clocked the pace of 200 randomly selected pedestrians on city streets in Vienna. They interviewed them and found that better educated and more affluent men walked faster then less privileged men even when they were not going anywhere in particular. This was not true of high-status women. The authors suggest that this goes back to the days when men hunted for their families, and, in the 90's, is a way of telling the opposite sex that you're a good provider.

The other studies are: A study reported in the current issue of the "Journal of Quantitative Criminology" giving statistics on the crack cocaine epidemic during the years 1995 to 1991; a study in "Social Science and Medicine" that showed that educated people live longer than those with less education; and a study in the latest "British Journal of Medical Psychology" comparing the poetry written by 40 diagnosed psychotics and 40 diagnosed normal people.


(1) What do you think about the explanation for affluent men walking faster? What would be your explanation?

(2) If you were doing such a study, how would you pick a random group of pedestrians?

(3) Do you think you would find the same results if you chose a sample from men and women walking down Fifth Avenue in New York City?

(4) No differences were found in the content, imagery, word choice or overall quality of the poems written by the psychotics and those written by the normal people. What might you conclude from this?

Math curriculum deals a message: students learn hazards of gambling.
The Boston Globe, 10 February 1996, p1
Tom Moroney

Harvard Medical School researchers have introduced a new mathematics curriculum in the Billerica (MA) public schools which aims to prevent addiction to gambling later in life. The hope is to make temptations like the lottery less attractive by teaching students how to think through the odds.

One exercise described here has students rank events in order of their statistical likelihood. The events include dying from a bee sting, being killed in a car accident and winning the Megabucks jackpot. With a one-in-12.3 million chance, the lottery turns out to be the least likely event.


(1) Do you think the researchers mean the chance that a bee sting turns out to be fatal, or the chance of that a randomly selected person will be stung and die? (For the latter: during what period?) Which of these is larger? How would each be estimated?

(2) Which makes a more reasonable comparison with buying a lottery ticket?

Faulty Arizona data highlight shortcomings of exit polling.
Washington Post, 29 Feb, 1996
Richard Morin

Soon after the polls for the Arizona primary closed, CBS, ABC and CNN incorrectly predicted that Dole would finish in third place. The networks predictions were based on an exit poll carried out for the news services by Voter News Service of New York. This exit poll, based on 2,102 randomly selected voters, gave 31% to Buchanan, 31% to Forbes and 29% to Dole. Current (unofficial) results give 33% for Forbes, 30% for Dole and 27% for Buchanan.

The sampling error for the poll is given as 3%. It is suggested that the margin of error could account for some but not all of the error. Murray Edelman, the editorial director of VNS said that exit polls have consistently overestimated the Buchanan vote. He suggested that this could be because Buchanan's supporters are more willing to be interviewed. He remarked that Buchanan's vote in the early rounds of exit polling has been even more exaggerated. Edelman remarked that different types of voters tend to vote a different times: affluent, white collar voters are more likely to vote in the morning, women and retired persons in the afternoon and working class voters after work in the evening. This also contributes to the unreliability of early exit polls.


(1) The margin of error is usually given as the reciprocal of the square root of the sample size which, in this case, would give a margin of error of 3.8%. What is the justification for this calculation? Why do you think they gave 3% for this poll? If you used 3.8% as the margin of error could the difference observed be explained entirely in terms of margin of error?

(2) How should the margin of error for a poll be modified when there are more than two candidates and you are interested in estimating the difference in two candidates votes to see which is in the lead? (See Chance News 3.04 for a discussion of this problem)

(3) What do you think it means to say that the 2,102 voters in the exit poll were randomly selected?

You really can die of fright, study says.
The Boston Globe, 15 February 1996, p 3
Richard A. Knox

Results published in the current "New England Journal of Medicine" provide evidence that it is indeed possible to die from fright or emotional shock. The evidence was provided by records from the Los Angeles earthquake on January 17 1994. On that day, the number of sudden-death heart attacks in Los Angeles increased by a factor of 5, compared to the preceding days or to the same dates in earlier years. Cardiac deaths clustered in the first two hours after the quake and were more frequent nearer the epicenter. Physical exertion--running from a house or lifting debris--was a factor in only three of the 24 sudden-death heart attacks, leaving emotional stress as the most likely contributing factor in the others.

For several days following the quake there was a below-average rate of cardiac deaths, suggesting that the people who died were already on the brink of an attack, which the quake brought on a few days prematurely. But if the people are about to die anyway, what is the point of knowing that the attacks can be triggered by stress? Dr. James Muller of New England Deaconess Hospital says that "if we can cut the linkage between the trigger and the event, we have a novel method of prevention." For example, Muller has found that moderate exercise protects against attacks triggered by exertion, low aspirin doses protect against those triggered by anger, and beta-blocker drugs protect against those triggered by the stress of simply rising in the morning.


(1) What is the point of looking at deaths for the days preceding the quake compared to the same dates in previous years?

(2) What do you think of Dr. Muller's argument? In particular, what is novel in the finding that exercise can prevent heart attacks due to exertion?

(3) Does this story have anything to do with the discussion from the last edition of Chance News about whether the murder rate goes down during blizzards?

Lie detectors get new push; SJC to hear appeal for tests.
The Boston Globe, 6 February 1996, p 1
Anthony Flint

In Supreme Judicial Court tomorrow, a Cambridge public defender will ask that results of a polygraph test be admitted as evidence in his client's appeal of armed robbery charges. At least 5 federal judges have already ruled such evidence admissible, apparently in the wake of the 1993 US Supreme Court ruling in Daubert v. Merrill Dow Pharmaceuticals, which gave judges more discretion in admitting scientific evidence. Previously, such evidence had to meet the standard of "general acceptance of the scientific community".

Critics call polygraphs "junk science", which can be easily manipulated by defendants who learn to beat the test or by fraudulent examiners. Proponents argue that, with new computer technology, the test can have an accuracy rate of up to 95%.


What kinds of errors can be made in a polygraph test? What does an "accuracy rate" of 95% mean?

Donald Richards sent us the following example of the use of probability in the best seller book "Debt of Honor" by Tom Clancy. He found that the students in his Chance course enjoyed discussing this example in relation to the binomial distribution.

The 1994 edition of "Debt of Honor" contains the following discussion on pages 686- 687

There were ten target points -- missile silos, the intelligence data said, and it pleased the Colonel [Zacharias] to be eliminating the hateful things, even though the price of that was the lives of other men. There were only three of them [bombers], and his bomber, like the others, carried only eight weapons [smart bombs]. The total number of weapons carried for the mission was only twenty-four, with two designated for each silo, and Zacharias's last four for the last target. Two bombs each. Every bomb had a 95% probability of hitting within four meters of the aim point, pretty good numbers really, except that this sort of mission had precisely no margin for error. Even the paper probability was less than half a percent chance of a double miss, but that number times ten targets meant a 5% chance that [at least] one missile would survive, and that could not be tolerated.''

(Note: We found this paragraph a little clearer when we read, later in the book, that the first bomber aimed at targets 1 through 8, the second 3 through 10 and the 3rd took the second shots at 1,2,9, and 10 and used the other 4 to take out a dam).


(1) Is the probability reasoning of Zacharias (Tom Clancy) correct and are his and calculations correct?

(2) Consider ten Bernoulli trials, with p the probability of success and q = 1-p the probability of failure on each trial. When is is appropriate to estimate the probability of at least one failure in ten trials as 10q?

(3) Is it reasonable to assume that the success of the bombs are independent? Why were the targets assigned the way they were?

Ask Marilyn.
Parade Magazine, 18 February 1996, p 18
Marilyn vos Savant

A reader asks:

"Say I have a wallet that contains either a $2 bill or a $20 bill (with equal likelihood) but I don't know which one. I add a $2 bill. Later I reach into my wallet (without looking) and remove a bill. It's a $2 bill. There's one bill remaining in the wallet. What are the chances that it's a $2 bill?"

Marilyn gives the answer as 2/3, by talking through the (equally likely) cases that could have led to the removal of a $2 bill and noting that two out of three correspond to the $2-$2 scenario (as opposed to $20-$2).


(1) Does this problem seem more realistic than the usual formulation of drawing balls from an urn?

(2) Some people like to try to make sense out of this question even when you have no idea about the probability that the original bill was a 2$ or a $20 bill. Could you give sensible answer in this case?

Study Examines Race and Justice in California.
The New York Times, 13 Feb. 1996, A12
Fox Butterfield

A new study from the Center on Juvenile and Criminal Justice in San Francisco, a research and advocacy group, found that almost 40% of black men in their 20's in California are imprisoned, on probation, or on parole on any given day. The new study is the latest in a series of reports in the past few years showing that young black men are being incarcerated at a rate far out of proportion to their number in the overall population. Last fall, a study found that, nationally, 1/3 of black men in their 20's were under the control of the justice system, an increase from five years ago when the number was 25%.

By contrast, last year only 5% of white men in California in their 20's and 11% of Hispanic men of that same age group were in the criminal system.

Vincent Shirardi, the study's author, attributes the large number to tougher punishment for the use of crack cocaine; harsh new sentencing laws; the prison construction boom; poverty; lack of good jobs; and poor education in inner cities. He also predicts that California's new "three strikes" sentencing law will increase the number of young black men in prison. Of 1,000 cases, blacks were being sentenced at 17 times the rate of whites under the new law.

Criminologists offer different views on what the data represents. James Q. Wilson, professor of management at UCLA, said that, although the figures were troubling, "if you set aside the arrests for crack cocaine, they are not the result of bias in the criminal justice system." By contrast, Alfred Blumstein, a Carnegie Mellon University criminologist, said that disproportionate figures result from the war on drugs, in which the police have focused on the inner city rather than on the suburbs.


What data would you look at to decide if blacks are being treated unfairly under the new "three strikes" law?

Low taxes, high death rate for smokers.
Indianapolis Star, 1 Feb. 1996, A8
Andrea Neal

Smoker statistics.
Indianapolis Star 8 Feb. 1996, A9
Letter to the editor from James M. Hall Jr.

The first article reports that recent data released by the Centers for Disease Control showed that Indiana ranks seventh in the number of deaths linked to smoking. At the same time, Indiana has the eighth lowest excise tax on cigarettes. The article quotes David Richards, the chairman of the public affairs committee of the American Heart Association's Indiana chapter, as saying that:

there appears to be a definite correlation between the high prevalence of smoking and ensuing deaths and those states with low excise taxes. If you look at the eight states with the lowest taxes on cigarettes, you will see that all of them are grouped in the higher rates of deaths related to smoking. Lower prices simply stimulate the purchase and consumption of cigarettes.

Commenting on this article, James Hall writes:

I took the time to plot the data, released recently by the Centers for Disease Control and Prevention, for all states on a graph that shows the percent who smoke vs. the per pack tax. The points are randomly scattered and there appears to be little if any correlation between the state tax now imposed on cigarettes and the percentage who smoke. "

He goes on to note that: "Nevada has the highest percent who smoke and a relatively high tax and Utah the lowest percentage who smoke of all the states and a tax lower than many states." He suggests that this might be because gamblers need to smoke and Mormons are trained at home not to smoke.


(1) Can David Richards and James Hall both be right about the data?

(2) Why do you think that Neal compared tax with deaths due to smoking and Hall considered tax with percent who smoked? Which is more appropriate?

(3) How do you think they estimate the death rate due to smoking?

Note: We also thought it would be interesting to look at the data. The correlation between tax and smoking rate is -0.34 and between tax and death rate is -0.18. The correlation between smoking and death rate is 0.68 You can find the data on the Chance Web site in Class 11 of the current Princeton Chance course.

New AIDS Therapies Arise, But Who Can Afford the Bill?
The New York Times, A1, 6 February 1996
Lawrence K. Altman, M.D.

With the revelation last week of the potency of new AIDS therapies and tests, many doctors, researchers, and patients worried about the costs of these new treatments and who will be able to afford them.

In his article, Lawrence Altman reports that the new combination anti-HIV. therapy, consisting of a protease inhibitor and AZT and 3TC, suppresses the amount of HIV. in the body to levels undetectable by current tests. The catch, however, is that such therapy may cost from $12,000 to $18,000 a year. For patients with advanced AIDS, however, costs may rise as high as $70,000 per year.

How much treatment costs will rise is not known. One protease inhibitor, saquinavir, costs $7,000 a year. The makers of two new protease inhibitors, indinavir and ritonavir, have not commented on how much the drugs will cost. In addition, a new test that can more accurately predict the course of HIV. infection was introduced last week and is expected to cost $200 per test, but it has to be performed at least four times a year.

Many doctors worry that budgets may not rise, even though costs will undoubtedly escalate. Dr. Harold Jaffe, an official at the "Centers for Disease Control and Prevention", said that "because of the patient advocacy for AIDS, there will be a lot of pressure to make the standard of care a very expensive one." Dr. Jaffe also commented that many hospitals have fixed pharmaceutical budgets and wondered which drugs hospitals will be able to supply patients.

Currently, drug costs for AIDS treatments are picked up by some private insurance companies. Medicaid also covers AIDS treatment, but the number of drugs covered each month may be limited. In addition, the Ryan White Act, a Federal drug assistance program, also helps patients with some of their drug costs.


Do you think that the cost of a drug should enter in the treatment of a patient? If so, what else should be taken into account in deciding whether to use an expensive drug?

Can retiree's safety net be saved?
The New York Times, Feb. 18, 1996, Sec. 3, p. 1
Peter Passell

In 1983 it was clear that the amount being taken in by payroll taxes would soon not cover the amount of Social Security payments necessary. Congress made modest decreases in social security benefits and increased taxes on the benefits intended to allow payroll taxes to cover Social Security payments for the next 75 years. Now new projections suggest that this will be the case only for the next 17 years and that the present 12.4% (employee and employer combined) being collected is 2% short of the amount that would have to be collected to meet the 75 year goal. If nothing is done about this, by 2022 benefits promised would have to be cut by about 1/3.

Unlike the situation in 1983, the problems are far enough in the future that the solution does not have to be started immediately. But the longer it is postponed the harder the problem will be to solve.

No one expects anything to be done immediately, but members of the Social Security Administration's advisory council are considering various solutions to the problem. The current social security surplus of over 500 billion is held in treasury bonds making 2.7%. Historically this money would have made more like 7% if held in stock funds. So one possibility is to hold the money in a government-run mutual fund. Of course this is gambling with the future. A more extreme suggestion is to move to a private system where workers would be provided money directly which they would have to invest for their own retirement.

There is always a lot of argument about whether workers get back as much as they put in. To show that the answer is not simple the article state that:

A single average-income worker, born in 1930, can expect to get back about 90% of the total payroll tax paid, plus interest, while the same kind of worker, born in 1950, will end up with just 55%.

A single low-income worker, born in 1930, can expect to get back about 120% of his or her contribution, while a married couple with just one low-income worker, born in that year, can expect to reap 235%.


(1) Why do you think the 1983 estimates were so wrong? Do you think estimates being made now will be any better?

(2) Why do demographic changes have such a large effect on the success of the social security system?

Sorting out contradictory findings about fat and health.
The New York Times, Feb. 14, 1996, C8
Jane E. Brody

A new Harvard study has found no evidence, among a number of studies of more than 335,000 women, that a diet with less than 20% of calories from fat reduced a woman's risk of developing breast cancer. Also, risk was not related to the types of fats the women consumed.

Jane Brody, however, cautions that diet should not be totally excluded as a factor in breast cancer. She lists the following topics yet to be explored:

The idea that fat may influence the risk of breast cancer arose from international comparisons. Breast cancer is much less common in Asia and in poor countries whose populations have a low-fat diet. Brody lists several reasons why this might be so:


What message to you think Jane Brody is trying to give in
this article?

HIV risk in boxing too great.
The Boston Globe, 13 Feb. 1996, Sports p. 62
Richard A. Knox

The positive HIV test for boxer Tommy Morrison has once again raised the question of mandatory testing for certain athletes.

AIDS experts are quoted as saying that boxing is really different than other sports. The business of boxing is producing blood. Even though there has never been a documented case of an athlete being infected with the HIV virus through contact in a sporting event, these experts feel that the risk for boxing is real.

A year ago scientists from the Center for Disease Control estimated that the chances of professional football players getting HIV on the field were less than one in every 85 million game contacts. However, they documented two cases where it had been transmitted through bloody fist fights.


(1) How do you think they determined the odds for a professional football player to be infected with AIDS on the field?

(2) Some experts argued that the risks of getting AIDS from boxing is not significant and whatever small risk there is it's nothing compared to the risk of serious brain damage. What do you think of raising the issue of brain damage in this argument?

Chemicals in Food? A Panel of Experts Finds Little Danger.
The New York Times, A1, 16 February 1996
Jane E. Brody

On average, about 6,000 chemicals, synthetic and natural, are deliberately or inadvertently added to foods. The National Research Council, a division of the National Academy of Sciences, has concluded that there are many natural and synthetic carcinogenic chemicals in foods, but their importance as cancer-causing agents is minimal compared with the over consumption of calories and fat.

In a new report, "Carcinogens and Anticarcinogens in the Human Diet," the panel concluded that about 1/3 of the 1.35 million new cancer cases in the nation each year could be traced to diet but probably not to natural or synthetic chemicals in significant numbers. Both naturally occurring and synthetic food chemicals are present in the human diet at such low levels that they are unlikely to pose a serious cancer risk.

The research panel also concluded that naturally occurring carcinogens greatly outnumber synthetic ones and make a larger contribution to increased cancer risk. Natural carcinogens are unavoidable, but the more than 100 known synthetic carcinogens in foods are avoidable.


This seems like another example of being asked not to worry about A that we can do something about, because the risk from the related B that we can't do much about is so much greater. What do you think about this?

Send comments and suggestions to jlsnell@dartmouth.edu


CHANCE News 5.03

(4 Feb. 1996 to 27 Feb. 1996)