Question

Please answer the following question?

An instructor randomly selects one of the pianists to play first part of the duet from a group of `5` pianists that includes `2` boys and `3` girls. What is the probability of selecting a boy for first part of duet and a girl for the second part of the duet? How the probability changes if second pianist is different?

Answer 1

Please see below.

Explanation:

As the instructor randomly selects one of the pianists to play first part of the duet from a group of `5` pianists that includes `2` boys and `3` girls,

the probability of selecting boy first is given by

`P("boy first")=2/5`

as he selects a pianist to play second part of the duet,

the probability of selecting girl second is given by

`P("girl second")=3/5`

Hence `P("boy first")*P("girl second")=2/5xx3/5=6/25`

However, probability of selecting a boy first is `2/5` and then a girl, which is a different pianist should be `3/4`, as he has to select one of the girls among `1` boy and `3` girls.

Hence `P("boy first and girl second")=2/5xx3/4=6/20=3/10`

As `P("boy first")*P("girl second")!=P("boy first and girl second")`, so the events are not independent.