Respuesta :
Using the hypergeometric distribution, it is found that there is a 0.1539 = 15.39% probability that all the four students like pizza.
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.
For this problem, the values of the parameters are given as follows:
N = 15, n = 4, k = 10.
The probability that all the four students like pizza is P(X = 4), 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 = 4) = h(4,15,4,10) = \frac{C_{10,4}C_{5,0}}{C_{15,4}} = 0.1539[/tex]
0.1539 = 15.39% probability that all the four students like pizza.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
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