Question

a committee of 6 males and 6 females. a sub committee of 4 is selected at random.  

1. What is the probability that exactly one of these chosen are women?
2. What is the probability that at least one of these chosen is a women?

Answer 1

solution:

commitee consisting of

male = 6

female = 6

total person = 12

a sub commitee of 4 member is selected at random

so, a commitee of 4 members can be selected in of total 12 in members = ways

a) we have to find the probability of exactly one of four selected members are female

so we can select 3 male and 1 female

selecting 3 male out of 6 =

selecting 1 female out of 6 =

so required probability = (20*6)/495 = 0.2424

b)

probability that atleast one of those 4 members is a female

P(atleast one is women) = 1 - P(none is women among 4)

selecting none women (4 male) out of 6 is

P(none is women among 4) = 15/495 = 0.0303

P(atleast one is women) = 1 - 0.0303 = 0.9697