Question

A committee of three is to be selected at random from five married couples. What is the probability that the committee contains an odd number of women or an odd number of men?

Answer 1

`100%`

Explanation:

If there are:
`color(white)("XXX")0` women `rarr` there is an odd number of men (`3`)
`color(white)("XXX")1` women `rarr` there is an odd number of women (`1`)
`color(white)("XXX")2` women `rarr` there is an odd number of men (`1`)
`color(white)("XXX")3` women `rarr` there is an odd number of women (`3`)

There will always either be an odd number of women or and odd number of men.