Respuesta :
Using the hypergeometric distribution, there is a 0.4894 = 48.94% probability of selecting none of the correct six integers in a lottery.
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, we want to take 6 numbers from a set of 56, hence the values of the parameters are:
N = 56, k = 6, n = 6.
The probability of selecting none of the correct six integers in a lottery is of P(X = 0), 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 = 0) = h(0,56,6,6) = \frac{C_{6,0}C_{50,6}}{C_{56,6}} = 0.4894[/tex]
0.4894 = 48.94% probability of selecting none of the correct six integers in a lottery.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
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