MathDB

4

Part of 1992 ITAMO

Problems(1)

italian jury of n persons , probability a fixed juror is a part of the majority

Source: 1992 ITAMO p4

1/31/2020
A jury of 99 persons should decide whether a verdict is guilty or not. Each juror votes independently with the probability 1/21/2 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 nn 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 1/21/2, respectively. (For n=2kn = 2k, k+1k +1 votes are needed for a majority.)
probabilitycombinatorics