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a. You are on a jury and the prosecution tells you that the accused has the same

ID: 3060178 • Letter: A

Question

a. You are on a jury and the prosecution tells you that the accused has the same blood type as evidence found at the crime, and only one in a thousand people have that type. The defense attorney points out that the police tested samples from 200 people. If everyone tested was a random innocent person, what is the probability that a 1/1000 match would have been found by chance? b. What if there were 10 distinct samples found at the scene, each matching a separate 1/1000 of the population? That is, what is the probability that a 1/1000 chance match would have been found between one of the randomly tested individuals and one of the samples?

Explanation / Answer

Solution-

1. Let X bet the random variable of the number of persons found accussed then X must follow binomal distribution with parameters -

n = sample size = 200 and p = 1/1000 = 0.001

Required probability = P(X=1)

= 200c1 * 0.0011* ( 1-0.001)199

= 0.1639.

2. Let Y bet the random variable of the number of samples with one accussed, then Y must follow binomial random variable with parameters-

n = 10 and p = 0.1639

Required probability= P(Y=1)

= 10c1 * 0.16391 * (1-0.1639)9

= 0.3273

Answer

TY!

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