Answer :
The probability that the committee includes all 3 women is 0.00018
In this question, we have been given there are 97 men and 3 women in an organization.
A simple random sample of 5 people is taken to form a committee.
We need to find the probability that the committee includes all 3 women.
Total number of people in the organization: 97 + 3 = 100
Usinng combination formula the possible number of 5 people committee:
100C5
= 100! / 5!(100 - 5)!
= 75287520
The number of outcomes for the committee includes all 3 women would be:
5C3 = (97C2)*3
= 13968
So, the probability that the committee includes all 3 women would be,
P = 13968 / 75287520
P = 0.00018
Therefore, the required probability is 0.00018
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