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# CLASS 19

## HANDOUTS:

``Jury to hear statistics on genetic fingerprints", ``Mathematical challenge to DNA testing in rape case", Rules for blackjack and roulette.

## DISCUSSION:

DNA fingerprinting in the courts.

Read the two newspaper articles and answer the following questions.

DNA fingerprinting uses the fact that at certain well defined places in a your DNA there are repetitions of a specific DNA pattern, and the number of repetitions of this pattern varies from person to person. For example, assume that the pattern TGA occurs at this place a number of times ranging from 1 to 30. Since these are in chromosomes and chromosomes come in pairs you actually have two such sequences. You got one from your mother and one from your father. Thus you might have gotten the sequences TGATGATGA from your mother and the sequence TGATGATGATGATGA. We could describe this as a 3,5 pair.

If you were the suspect in the case, the FBI wants to find the probability that there is another person in the population with this exact same pair of repetitions. To do this they collect data about 1000 people obtaining 2000 pairs of repetitions. They then find the proportion of times each number between 1 and 30 occurs in these 2000 pairs.

Assume that they find that a repetition of 3 occurs 10 percent of the time and 5 occurs 20 percent of the time. Then they say that the probability that a randomly chosen person from this population matches your 3,5 pair is 2 x .1 x .2 = .04. (The 2 comes from the fact that you could have gotten 3 from your father and 5 from your mother or 3 from your mother and 5 from your father. They do this at about 5 different places in your DNA and again multiply the probabilities to get the probability of a complete match and end up with a number like 1 chance in a trillion that a randomly chosen person matches your 5 pairs exactly.

Question: Would you believe this one chance in a trillion number? What assumptions do you think have been made to justify it? How would you test these assumptions?

Question: If you were on a jury and you believed a suspect had one chance in a trillion of being innocent, would you consider this guilt beyond a reasonable doubt?

The Sunday Telegraph article says that the odds quoted actually represent the probability of getting so good a DNA match from a person unconnected with the crime, but what the jury is trying to decide is the probability of a person being unconnected with the crime, given so good a DNA match.

Question: What does this mean? Why is it different?

One last percentage question: From November 17, The New York Times.

As part of the biggest revamping in the 53-year history of the Government survey that determines the nation's official jobless rate, researchers at the Labor Department have discovered a bias in the survey under which many women who were seeking jobs were erroneously described as homemakers, and therefore not counted as being in the work force.

Under the redesigned survey, which tries to wipe out any bias, the nation's average unemployment rate in the 12 months through August was 7.6 percent, a half-point above the 7.1 percent that the department had reported. The rate for women was 6.8 percent, rather than 6.0 percent; for men, the figure went to 6.9 percent from 6.7.

Question: In the new survey the unemployment rate for women (6.8%) and for men (6.9%) were both less than the overall unemployment rate (7.6%). Is this possible?

One last Marilyn vos Savant question: Parade Magazine, November 14

There are five cars on display as prizes, and their five ignition keys are in a box. You get to pick one key out of the box and try it in the ignition of one car. If it fits, you win the car. What are your chances of winning a car?

## CHANCE FAIR

The CHANCE Fair will take place in Alumni Hall on Sunday December 5 from 4 to 6 P.M. All final projects must be completed and ready for display at the beginning of the Fair. In addition to your display, your project should have a more detailed explanation of what you studied or what experiments you did to be handed in at the Chance Fair. No extensions will be allowed without an official medical excuse.

There will be boards on which to put your posters and the management will provide tape for sticking your posters to these boards. You can come a little early to do this. Anything else you need is up to you. If you need a computer please bring your own if possible. If you have any special needs such as a computer, a connection to the network, a VCR etc. we must know at least two days in advance. Make you posters colorful and informative!

If you have not handed in your Post Course Survey and Course Evaluation be sure to do so at the Chance Fair.

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laurie.snell@chance.dartmouth.edu