Question

A committee of 3 needs to be selected from a group of 3 gentlemen and 4 ladies. what is the probability that the committee will consist of at least one gentleman?

Answer 1

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Answer 2

Answer:

Given

3 gentlemen

4 ladies

Total =7

A committee of 3 needs to be selected and the committee will consist of at least one gentleman

So the possibilities are

* 1gentleman & 2ladies

*2gentleman & 1 ladies

*3gentleman& no ladies

So the

n(event) =³c1x ⁴c2 + ³c2 x⁴c1 + ³c3x⁴c0

= 3*6+ 3*4 +1*1

=18+12+1

=31

Total number of ways

n(s) =7c3

=35

Therefore the probability that the committee will consist of at least one gentleman is

Therefore the probability that the committee will consist of at least one gentleman isN(p) =n(e) /n(s)

Therefore the probability that the committee will consist of at least one gentleman isN(p) =n(e) /n(s) =31/35