Question

Five persons are chosen at random from a group of ten persons consisting of four men and six women. Calculate the probability that there are more women chosen than men.

Answer 1

Total persons = 10

Total men = 4

total women = 6

number of persons to be selected = 5

condition = women should be more than men

Thus , the combination would be 5 women and 0 men , 4 women and 1 man , 3 women and 2 men

Total number of ways to select 5 people from 10 people = 10C5

P(event ) = number of favourable outcomes / total number of outcomes

P(5 women and 0 men selected ) = {6C5 * 4C0} / 10C5= 6 / 252

P(4 women and 1 men selected ) = {6C4 * 4C1} / 10C5 = 60 / 252

P(3 women and 2 men selected ) = {6C3 * 4C2} / 10C5 = 120 / 252

P(chosing 5 persons from 10 persons with more women than men ) = 6/252 + 60/252 + 120/252 = 186/252

P(chosing 5 persons from 10 persons with more women than men)= 0.738095