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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
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