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?

1 Answer
Shwetank Mauria
Aug 2, 2017

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.

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