Concept explainers
To calculate: The probability that committee has at least three women.
Answer to Problem 44E
The probability that committee has at least three women is
Explanation of Solution
Given information:
A subcommittee of 5 members is to be selected from a committee of 6 women and 7 men.
Formula used:
Probability of an event E is
If there are n objects taken r at a time then combination is defined as
Calculation:
Consider the provided information that subcommittee of 5 members is to be selected from a committee of 6 women and 7 men.
Since, order is not important use combination.
Recall that if there are n objects taken r at a time then combination is defined as
Recall that probability of an event E is
The probability that committee has at least three women means the committee can have either 3 or 4 or 5 women to form a 5 member committee.
If there are 3 women then there are 2 men.
If there are 4 women then there is 1 man.
If there are 5 women then there are 0 men.
The events are mutually exclusive events.
The probability is,
Thus, the probability that committee has at least three women is
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