Question
upstudy study bank question image url

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.)

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

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

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 .

Related Questions

Latest Probability Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy