Friday, April 28, 2006

The crazy juror

We have a 3-person jury. I know jury is not a 3-person team, but lets just stick to our problem for now. In this 3-person jury, there are 2 jurors who are very serious. However there is a crazy juror, the third juror, who likes to flip a coin and based on the outcome agree with either juror's decision. Now, each of the serious jurors can independently give the correct decision with a probability of 'p'. You are called to inspect this jury and make suggestions. You wonder if a single-person-jury with a correct-decision making probability of 'p' is better off than this 3-person jury with the crazy flippant juror. What is your observation and what do you say to the judge about the 3-person jury?

Level: Easy


Anonymous balaji said...

the probability of a correct decision by the jury is same as that of a serious juror.

the probability of correct descision wirh single juror is p.

with three jurors, the probability is

p^2 + 2x p(1-p)x1/2 = p^2 +p - p^2 = p

p^2 is the probability that both the serious jurors make the right decision.

the probability of one of the serious juror not making the right decision is 1-p. and there is a half chance that that the third person agrees with the right person.
therefore probability of a right decision when the two serious jurors do not concurr. is p(1-p)x1/2. but since two serious jurors are there, the whole thing is multiplied by 2.

therefore, probability of a right decision is p in either case.

10:47 PM, April 28, 2006  
Anonymous Vikram said...

looks like we are done here :)

1:49 AM, April 29, 2006  
Blogger silentkiller said...

oh damn! i thought it wasn't answered yet :) yeah, it's the same, probability p in both cases.

psst.. update the solved puzzles column :D

7:19 AM, April 29, 2006  
Blogger Karthik Nagaraj said...

Ok, Balaji has got the right answer. Good thinking guys. This was a typical problem of 'Conditional Probability'. Very often people tend to miss multiplying (p-1) to make sure the other sane juror does not agree with the other other sane juror. Ok I think time for a new one!

Tejas (Silentkiller) - bad luck, keep trying and you can get it before anyone else next time. Good luck

This puzzle is SOLVED!

10:35 AM, April 29, 2006  

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