Question
From a group of 10 boys and 13 girls, a committee of 5 students is chosen at random.
a. What is the probability that all 5 members on the committee will be girls?
b. What is the probability that all 5 members of the committee will be boys?
c. What is the probability that there will be at least 1 girl on the committee?
a. The probability that all 5 members on the committee will be girls is
(Type an integer or a simplified fraction.)
a. What is the probability that all 5 members on the committee will be girls?
b. What is the probability that all 5 members of the committee will be boys?
c. What is the probability that there will be at least 1 girl on the committee?
a. The probability that all 5 members on the committee will be girls is
(Type an integer or a simplified fraction.)
Ask by Elliott Malone. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that all 5 members on the committee will be girls is
.
Solution

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The Deep Dive
To find the probabilities, we will first determine the total number of ways to choose a committee of 5 members from the group of 23 students (10 boys and 13 girls).
The total combination of choosing 5 students out of 23 can be calculated using the combination formula:
Here,
and
.
Total combinations:
Now, let’s answer the questions:
a. Probability that all 5 members will be girls:
The number of ways to choose 5 girls from 13 is:
The number of ways to choose 5 girls from 13 is:
The probability is:
b. Probability that all 5 members will be boys:
The number of ways to choose 5 boys from 10 is:
The number of ways to choose 5 boys from 10 is:
The probability is:
c. Probability that there will be at least 1 girl on the committee:
We can find this by taking the complement of the probability that there are no girls (i.e., all boys):
We can find this by taking the complement of the probability that there are no girls (i.e., all boys):
Using our previous result:
In conclusion:
- a. The probability that all 5 members on the committee will be girls is
. - b. The probability that all 5 members of the committee will be boys is
. - c. The probability that there will be at least 1 girl on the committee is
.