Question

Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 56.

Answer 1

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:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,56,6,6) = \frac{C_{6,0}C_{50,6}}{C_{56,6}} = 0.4894$

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 brainly.com/question/24826394

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