In a sample of 2016 US adults 242 said Richard Nixon was the

In a sample of 2016 U.S. adults, 242 said Richard Nixon was the worst president since World War II. Three U.S. adults are selected at random without replacement. Find the probability that all three adults say Richard Nixon was the worst president since World War II. Find the probability that none of the three adults say Richard Nixon was the worst president since World War II. Find the probability that at most two of the three adults say Richard Nixon was the worst president since World War II. Which of the events can be considered unusual? Explain.

Solution

242*241*240/(2016*2015*2014) =0.001710876

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Number of non worst president since World War II = 2016-242 =1774

(1774*1773*1772)/(2016*2015*2014) =0.6812414

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1-P(all three adults say Richard Nixon was the worst president since World War II)

=1-0.001710876

=0.9982891

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all three adults say Richard Nixon was the worst president since World War II is considered unusual because the probability is less than 0.05