Using the hypergeometric distribution, it is found that there is a 0.3548 = 35.48% probability that she packs at least one pair of high heels.
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, we have that:
- She has 31 pairs of shoes, hence N = 31.
- She has 6 pairs of high heels, hence k = 6.
- She selects two pairs, hence n = 2.
The probability that she packs at least one pair of high heels is given by:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[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(0,31,2,6) = \frac{C_{6,0}C_{25,2}}{C_{31,2}} = 0.6452[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.6452 = 0.3548[/tex]
0.3548 = 35.48% probability that she packs at least one pair of high heels.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
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