Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Using the hypergeometric distribution, it is found that there is a 0.6 = 60% probability Bob is on the committee.
The members of the committee are chosen without replacement, hence the hypergeometric distribution is used.
What is the hypergeometric distribution formula?
The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- There are 5 people, hence N = 5.
- 3 will be chosen, hence n = 3.
- Bob is one of the people, hence k = 1.
The probability Bob is on the committee is P(X = 1), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,5,3,1) = \frac{C_{1,1}C_{4,2}}{C_{5,3}} = 0.6[/tex]
0.6 = 60% probability Bob is on the committee.
You can learn more about the hypergeometric distribution at brainly.com/question/4818951
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
