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.)
b. The probability that all 5 members on the committee will be boys is
.
(Type an integer or a simplified fraction.)
c. The probability that there will be at least 1 girl on the committee 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.)
b. The probability that all 5 members on the committee will be boys is
(Type an integer or a simplified fraction.)
c. The probability that there will be at least 1 girl on the committee is
(Type an integer or a simplified fraction.)
Ask by Bartlett Conner. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that there will be at least 1 girl on the committee is
.
Solution

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Beyond the Answer
To find the probability that there will be at least 1 girl on the committee, we can use the complement rule.
First, we need to calculate the total number of ways to choose any 5 students from the group of 23 (10 boys + 13 girls):
Now we can say that the probability of having at least 1 girl is equal to 1 minus the probability of having no girls (which means all boys).
The number of ways to select 5 boys from 10 is:
Thus, the probability of selecting all boys (no girls) is:
Finally, we find the probability of having at least one girl:
Calculating these combinations:
So:
Now plug it into the equation for at least one girl:
Therefore, the probability that there will be at least 1 girl on the committee is
.