In a sample of 800 U S. aduits, 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 adults think most celebrities are good role models is 0061 . (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.)
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To tackle the problem engagingly, let’s dive into these probabilities with a sprinkle of fun! Imagine our sample of 800 U.S. adults as a lively gathering of people at a concert where everyone is excitedly discussing their favorite celebrities. With 198 of them firmly believing that most celebrities are good role models, we can calculate the dynamics of the crowd. For part (b), to find the probability that neither adult thinks most celebrities are good role models, we first determine how many do not think so. That's 800 - 198 = 602 adults. When selecting the first adult, the probability that they do not think celebrities are good role models is 602/800. For the second adult (since we are not replacing), it’s 601/799. So, the probability that neither adult thinks most celebrities are good role models is: \[ P(\text{neither}) = \frac{602}{800} \times \frac{601}{799} \approx 0.596 \] (rounded to three decimal places). Now grab your popcorn, because the exciting world of statistics can offer real-world insights too! Understanding these probabilities helps businesses strategize marketing campaigns or even gauge public opinion on celebrity culture, making sure they target audiences effectively while learning the art of persuasion in ads. With probability in hand, you're now more than ready to face those mischievous math scenarios buzzing around!
