Question

In: Statistics and Probability

In a sample of 1100  U.S.​ adults, 203 think that most celebrities are good role models. Two...

In a sample of 1100  U.S.​ adults, 203 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.)

Solutions

Expert Solution

Given,

In a sample of 1100 U.S.​ adults, 203 adult people think that most celebrities are good role models

Therefore,

Probability that a U.S. adult person think that most celebrities are good role models, p = 203/1100

Probability that a U.S. adult person does not think that most celebrities are good role models = 1 - p = 1 – (203/1100) = 897/1100

Two U.S. adults are selected at random from the population of all U.S. adults Without Replacement

Answer a:
Probability that both adults think that celebrities are good role models = p^2 = (203/1100)^2

                                                                                                                = 0.034

Answer b:
Probability that neither adult thinks that celebrities are good role models = (1 – p)^2 = (897/1100)^2 = 0.665

Answer c:
Probability that at least one of the two adults thinks most celebrities are good role models = 1 - Probability that neither adult thinks that celebrities are good role models = 1 – 0.665 = 0.335

(All answers are rounded up to 3 decimal places)

orchestra answered 1 year ago
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