You are the jury consultant working in a large law firm that handles many crimin

Question

You are the jury consultant working in a large law firm that handles many criminal trials. Your firm is representing someone who is facing criminal charges. If convicted, your client could face a minimum of five years in prison. The criminal trial is to take place with either a judge or a three person jury. That is, a judge or a three person jury will rule on your client’s innocence. Each person (Judge or person in the three person jury) has the probability of making the correct decision p, where 0<p<1.

If the decision of the majority is final, which is preferable? A three person jury or trial by a judge? Consider the random variable X which counts the number of persons who decide correctly in a three person jury.

Explanation / Answer

P(Judge will make correct decision) = p

P(Jury will make correct decision)

= P(At least 2 out of 3 members make correct decision)

= P(Exactly 2 out of 3 members make correct decision) + P(3 out of 3 members make correct decision)

= 3p2(1 - p) + p3

= 3p2 - 2p3

= p(3p - 2p2)

Now,

(3p - 2p2) will always be less than 1 and therefore, the above quantity will always be less than p. Hence,

Judge is preferable.

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