In a sample of U.S. adults, 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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20-08-2020
Mathematics

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In a sample of U.S. adults, 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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Complete question is;

In a sample of 800 U.S. adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.adults, 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 ________?(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 _______?(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 ______? (Round to three decimal places as needed.)

Answer:

A) 0.062

B)0.564

C)0.436

Step-by-step explanation:

There are 800 US adults sampled and 199 think that most celebrities are good role models.

Now, two are selected without replacement.

Thus;

A) Probability that both adults think most celebrities are good role models would be = (199/800) × (198/799) = 39402/639200 = 0.062

B) we want to find probability that neither adult thinks most celebrities are good role models.

Now, since 199 out of 800 think that most celebrities are good role models..

Thus, number that doesn't think most celebrities are good role models = 800 - 199 = 601

probability that neither adult thinks most celebrities are good role models. would be = (601/800) × (600/799)= 180300/319600 = 0.564

C) We want to find the probability that at least one of the two adults thinks most celebrities are good role models.

Now, since we already have the probability that neither of them thinks most celebrities are good role models, we will just subtract that probability from 1.

Thus;

probability that at least one of the two adults thinks most celebrities are good role models = 1 - 0.564 = 0.436