Question

A committee of 3 members is to be made out of 6 men and 5 women. what is the probability that the committee has at least two women?​

Answer 1

Answer:

Step-by-step explanation:

the correct probability is 14/33.

Answer 2

SOLUTION

GIVEN

A committee of 3 members is to be made out of 6 men and 5 women.

TO DETERMINE

The probability that the committee has at least two women

EVALUATION

Total number of members = 6 + 5 = 11

Number of members to select = 3

The number of ways 3 members can be selected from from 11 members

$\displaystyle \sf{ = {}^{11}C_3 }$

Now the committee has at least two women

Then two cases arise :

Case A. 1 man and 2 women to select

Case B. 3 women to select

Case : A

1 man and 2 women to select

In this case total number of ways

$\displaystyle \sf{ = {}^{6}C_1 \times {}^{5}C_2 }$

Case : B

3 women to select

In this case total number of ways

$\displaystyle \sf{ = {}^{5}C_3 }$

Hence the required probability

$\displaystyle \sf{ = \frac{( \: {}^{6}C_1 \times {}^{5}C_2) + {}^{5}C_3}{ {}^{11}C_3} }$

$\displaystyle \sf{ = \frac{( 6 \times 10) + 10}{165 }}$

$\displaystyle \sf{ = \frac{70}{165 }}$

$\displaystyle \sf{ = \frac{14}{33 }}$

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