#10 ) In a case in Riverhead, New York, nine different crime victims listened to
ID: 3276450 • Letter: #
Question
#10 ) In a case in Riverhead, New York, nine different crime victims listened to voice recordings of five different men. All nine victims identified the same voice as that of the criminal. If the voice identifications were made by random guesses, find the probability that all nine victims would select the same person.
You should enter your answer as a decimal, not as a percent. Do not round, as your answer should be a terminating decimal.
Hint: We are looking for the probability that nine victims randomly picked the same person from a line-up. Let’s take this question one victim at a time:
The first victim doesn’t need to pick suspect #1, they could pick ANY suspect, if they are picking randomly. So what is the probability that the first victim picks SOMEONE? ANYONE?
Now let’s look at victim #2. What is the probability that they pick the same person as victim #1?
Now let’s look at victim #3. What is the probability that they pick the same person as victim #1?Etc.
Now let's look at victim #9. What is the probability that they pick the same person as victim #1?
Once you find all those probabilities, what rule would apply?
Referring to Question #10, does this constitute reasonable doubt?
Keep in mind that your calculation is the hypothetical situation that they all GUESSED the same person. The reality of the situation is that they DID identify the same person.
An answer of "Yes" means based on your calculations, you cannot be sure that when all nine victims identified the same person, that they identified the true criminal. In other words, you're not convinced the victims identified the correct person. If you were on the jury, you would issue a "Not Guilty" verdict.
An answer of "No" means based on your calculations, there is no reason to believe someone else did the crime - the victims identified the correct person. Provided the prosecuting attorney proved his/her case, you would return a verdict of "Guilty" if you were on the jury.
Yes
No
Explain why you choose YES or NO?
Explanation / Answer
ANSWER : We need to use the multiplication property of probability. Now since each victims choice should not be influence by the others we can assumed independence.
Probability that first victim randomly picks A is (1/5).
Probability that they all pick A is (1/5)^9.
But, there are 5 suspects that they can pick, so the probability that they all pick some one suspect (A or B or C or D or E) is 5 times = 5 * (1/5)^9 = 1/ (5^8) = 1 / 390625 = 0.00000256
Referring to Question #10, does this constitute reasonable doubt?
Answer- there is no reasonable doubt.
Now, for the last part,
"NO" because we are calculating the probability that all 5 victims will choose the same person. That comes out to be very low. It is a negation type problem. This means the same person is selcted by all victims with probability 0.00000256.So this means the chances that he is a crminal (according to the victims by listening voice)=1- 0.00000256= 0.99999744 i.e 99.99%.
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