Suppose there are two juries, one composed of just one person (Jury 1) and one c

Q: Suppose there are two juries, one composed of just one person (Jury 1) and one c

Both jury have equal chance of giving the correct answer. . The probability that 1st jury gives correct answer = p . The probability that 2nd jury gives correct answer : = probability that two votes are correct + probability that all votes are correct = P(1st and 2nd correct) + P(1st and 3rd correct) + P(3rd and 2nd correct) + P(all correct) =p*p*0.5 + p*0.5*(1-p) + p*0.5*(1-p) +p*p*0.5 =p*(1-p) + p*p =p

ID: 2967923 • Letter: S

Question

Suppose there are two juries, one composed of just one person (Jury 1) and one
composed of three people (Jury 2).
The one person in Jury 1 has a probability p of getting the correct verdict.
In Jury 2, two of the people each (independently) has a of probability p of getting the
correct verdict. The third juror sleeps through the trial and flips a (fair) coin to determine the verdict. The three-person jury now renders a decision based on the majority of votes.
Which of the two juries (if either) is better at reaching the correct verdict?

Explanation / Answer

Both jury have equal chance of giving the correct answer.

The probability that 1st jury gives correct answer = p

The probability that 2nd jury gives correct answer :

= probability that two votes are correct + probability that all votes are correct

= P(1st and 2nd correct) + P(1st and 3rd correct) + P(3rd and 2nd correct) + P(all correct)

=p*p*0.5 + p*0.5*(1-p) + p*0.5*(1-p) +p*p*0.5

=p*(1-p) + p*p

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Suppose there are two juries, one composed of just one person (Jury 1) and one c

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