Question
In a sample of 800 U S adults, 198 think that most celebrities are good role models Two 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 aduils think most celebnties are good role models is 0061 (Round to three decimal places as needed) (b) Find the probability that neither adull thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is 0566 (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 colebrities are good role models is (Round to three decimal places as needed)
Ask by Collins Fitzgerald. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) The probability that both adults think most celebrities are good role models is 0.061.
(b) The probability that neither adult thinks most celebrities are good role models is 0.566.
(c) The probability that at least one of the two adults thinks most celebrities are good role models is 0.434.
Solution
There are 800 U.S. adults, and 198 of them think that most celebrities are good role models. When selecting 2 adults without replacement:
Step 1. Compute the complementary counts:
• Number who think most celebrities are good role models: 198
• Number who do NOT think so: 800 − 198 = 602
(a) To find the probability that both adults think most celebrities are good role models:
Probability = (198/800) × (197/799)
Here 197 is used in the second fraction because one "good role model" respondent has already been chosen, leaving 197 remaining out of 799.
Calculating this gives approximately 0.061.
(b) To find the probability that neither adult thinks most celebrities are good role models:
Probability = (602/800) × (601/799)
Similarly, after one non-"role model" respondent is chosen (602/800), there remain 601 non-"role model" respondents out of 799.
Calculating this gives approximately 0.566.
(c) To find the probability that at least one of the two adults thinks most celebrities are good role models:
Probability = 1 − (probability that neither adult thinks so)
= 1 − [(602/800) × (601/799)]
= 1 − 0.566
≈ 0.434
So, the answers (rounded to three decimal places) are:
(a) 0.061
(b) 0.566
(c) 0.434
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Simplify this solution Mind Expander
Let's solve part (c) to find the probability that at least one of the two adults thinks most celebrities are good role models. We can do this by using the complement rule. The probability that at least one of the two adults thinks that most celebrities are good role models can be calculated as: P(at least one) = 1 - P(neither) We have the probability that neither thinks most celebrities are good role models from part (b), which is 0.566. So, P(at least one) = 1 - 0.566 = 0.434 Therefore, the probability that at least one of the two adults thinks most celebrities are good role models is **0.434** (rounded to three decimal places).
