Jury puzzle

[huy.duong@ctsu.ox.ac.uk]

Dear anh Tuan,

Not sure if I remember the problem
correctly, but if there is one juror with prob .5
of a correct verdict and two each with independent prob P
then I think you have the same chance as one juror with prob P.

Call the jurors A, B and C.

The prob of a correct verdict is

the prob of (A right, B right, C right) plus
------------(A right, B right, C wrong) ----
------------(A right, B wrong, C right) ----
------------(A wrong, B right, C right)=

              (P     *  P     * .5)+
              (P     *  P     * .5)+
              (P     *(1-P)   * .5)+
              ((1-P) *  P     * .5)=

               P^2 + P(1-P)=P,

ie same as one jury member with prob P of a correct verdict.

Huy