In a sample of 1100 U.S. adults, 203 think that most celebrities are good role models. U.S. adults are selected from this sample without replacement. Complete parts (a) through (c). (a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is nothing. (Round to three decimal places as needed.) (b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is nothing. (Round to three decimal places as needed.) (c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models is nothing. (Round to three decimal places as needed.)

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joaobezerra joaobezerra · Answer 1 · 2022-09-14T00:11:37+02:00

Using the hypergeometric distribution, the probabilities are given as follows:

a) 0.034 = 3.4%.

b) 0.665 = 66.5%.

c) 0.3352 = 33.5%.

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:

For this problem, the parameters are given as follows:

N = 1100, k = 203, n = 2.

In item a, the probability is P(X = 2), 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 = 2) = h(2,1100,2,203) = \frac{C_{203,2}C_{897,0}}{C_{1100,2}} = 0.034[/tex]

For item b, the probability is 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(0,1100,2,203) = \frac{C_{203,0}C_{897,2}}{C_{1100,2}} = 0.665[/tex]

For item c, the probability is:

P(X >= 0) = 1 - P(X = 0) = 1 - 0.665 = 0.335.

More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394

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