Question

A college professor found herself assigned to a committee of six people composed of four men and two women​ - Alice,​ Bonnie, Carl,​ Danny, Evan, and Frank. The committee had to select two officers to carry out the majority of its administrative work.

If the officers are selected at​ random, what is the probability that both officers are​ women?

*

What is the probability that at least one of the two officers is a​ woman?

Answer 1

Answer: a)
`(1)/(15)` b)
`(3)/(5)`

Explanation:

Since we have given that

Number of men = 4

Number of women = 2

So, number of selected people = 2

So, the probability that both officers are women would be

`(^2C_2)/(^6C_2)\\\\=(1)/(15)`

And the probability that at least one of the two officers is a woman would be

`(^2C_1* ^4C_1)/(^6C_2)+(^2C_2)/(^6C_2)\\\\=(2* 4)/(15)+(1)/(15)\\\\=(8)/(15)+(1)/(15)\\\\=(8+1)/(15)\\\\=(9)/(15)\\\\=(3)/(5)`

Hence, a)
`(1)/(15)` b)
`(3)/(5)`