Probability?

Question

In a Riverhead, New York, case, nine different crime victims listened to voice recordings of 5 different men. All 9 victims identified the same voice as that of the criminal. If the voice identifications were made by random guesses, find the probability that all 9 victims would sleect the sameperson. Does this constitute reasonable doubt?

Thanks a lot !! :)

Answer 1

You're looking at the probability of 9 independent events (the identifications) giving particular outcomes.

Since there are 5 suspects (let's say Suspects V-Z), the odds of randomly picking any of them is (1/5). So Victim A has a one in five chance of choosing Suspect X.

Now, Victim B will *independently* select Suspect X with the same probability: one out of five times. You multiply his 1/5 probability by the 1/5 probability of Victim A.

In other words, out of 25 identifications, Victim A would choose Suspect X 5 times (for 5/25 or a one in five probability), and of those 5 times, Victim B would independently choose Suspect X only 1 out of the 5 times (same probability). It would therefore take 25 rounds of identification for them to *both* randomly choose Suspect X at the same time.

Based on that pattern, figure out how many rounds of identification it would take to get 9 people to all choose the same guy out of the lineup of 5 suspects. (It's near 2 million, as KAL said)

Answer 2

You tell me!...the probability of 9 victims randomly picking the same voice out of five possibilities is about 1 in 2 million!