Question

Consider the following set of workers. Brian Stella Peter Larry Gary Laura Paul Anna Megan Janet If a committee of 5 workers is to be chosen, and Brian must be in the committee,what is the probability that (a) it must include exactly 3 males? (b) it must include at least 3 males?

Answer 1

There are 10 workers. 5 male and 5 female.

This is sampling without replacement.

a) Without Brian there are 4 males. We have to choose 2 males from 4 males. 2 females should be selected from 5.

The probability that committee  must include exactly 3 males is

b) The probability of  committee with 3 males (part (a)) is .

The probability of  committee with 4 males is .

The probability of  committee with 5 males is .

The required probability ( committee with vat least 3 males) is,