Question

In: Statistics and Probability

A committee of 4 is chosen at random from a group of 7 women 5 men....

A committee of 4 is chosen at random from a group of 7 women 5 men. Find the probability that the committee contains at least one man.

without replacement

Solutions

Expert Solution

Solution:

Given:

7 women

5 men

Total = 12

We have to make committee of 4 and find the probability that the committee contains at least one man.

P( the committee contains at least one man) =.............?

P( the committee contains at least one man) = 1 - P( the committee contains NO man )

P( the committee contains at least one man) = 1 - P( the committee contains all four women )

Thus first find:
P( the committee contains all four women ) = ........?

4 women from 7 women can be selected in 7C4 ways and any 4 persons can be selected from 12 people in 12C4 ways.

Thus

P( the committee contains all four women ) = 7C4 / 12C4

Use following combination formula to find number of combinations:

Thus

P( the committee contains all four women ) = 7C4 / 12C4

P( the committee contains all four women ) = 0.070707

Thus

P( the committee contains at least one man) = 1 - P( the committee contains all four women )

P( the committee contains at least one man) = 1 - 0.070707

P( the committee contains at least one man) = 0.929293

P( the committee contains at least one man) = 0.9293

( Round answer to specified number of decimal places)

orchestra answered 1 year ago
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