Question

What is the probability the students wearing skirts will be selected twice?

At a local school a teacher is trying to randomly select the type of bottoms a female is wearing to school that day. With a computer program, it is possible to draw the same outfit twice. What is the probability the students wearing skirts will be selected two times?
Shorts: 45
Skirts: 77
Pants: 82
Athletic shorts: 71

Answer 1

If we can pick the same student twice, `7/25xx7/25=49/625=7.84%`

If we can't pick the same student twice,
`7/25xx6/24=7/25xx1/4=7/100=7%`

Explanation:

There are `45+77+82+71=275` students

The probability of randomly selecting a student who is wearing a skirt is:

`P("student is wearing a skirt")=77/275=7/25`

If we are allowed to randomly select the same student twice, the probability is:

`7/25xx7/25=49/625=7.84%`

If we are not allowed to pick the same student twice, the second pick will have to account for one less students wearing a skirt, so the probability is:

`7/25xx6/24=7/25xx1/4=7/100=7%`