Tue
Aug
9
Answer: Tuesday Teaser #35
In order to answer this teaser, we need to calculate the probability of the three man jury coming to the correct verdict.
In order to come to a correct verdict, two of the three must independently reach the correct verdict. This happens when either:
- The two “serious” jurors come to the correct verdict; or
- The two “serious” jurors disagree, but the “flippant” juror comes to the correct verdict.
The first case has probability p*p = p^2. The second has probability 1/2 * [p(1-p) + (1-p)p].
Summing the totals, the total probability becomes p, exactly the same as that of the one man jury. This seems like a curious result given that the one man jury intuitively feels as though it should be more serious (and hence reliable) than the three man jury.
