MathDB

A jury of

9

persons should decide whether a verdict is guilty or not. Each juror votes independently with the probability

1/2

for each of the two possibilities, and noone is allowed to be abstinent. Find the probability that a fixed juror will be a part of the majority. In the case of a jury of

n

persons, find the values of n for which the probability of being a part of the majority is greater than, equal to, and smaller than

1/2

, respectively. (For

n = 2k

k +1

votes are needed for a majority.)

Problem Statement