Using the hypergeometric distribution, it is found that there is a 0.1538 = 15.38% probability that the top three finishers in the contest will all be seniors.
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 14 players in total, hence N = 14.
- Eight are seniors, hence k = 8.
- Three will be taken from the sample, hence n = 3.
The probability that all of them are seniors is P(X = 3), 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 = 3) = h(3,14,3,8) = \frac{C_{8,3}C_{6,0}}{C_{14,3}} = 0.1538[/tex]
0.1538 = 15.38% probability that the top three finishers in the contest will all be seniors.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
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