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Chapter 8: Problem 60
Give an example of two events that are not mutually exclusive.
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a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is \(\frac{365}{365} \cdot \frac{364}{565} .\) Explain why this is so. (Ignore leap years and assume 365 days in a year.) b. If three people are selected at random, find the probability that they all have different birthdays. c. If three people are selected at random, find the probability that at least two of them have the same birthday. d. If 20 people are selected at random, find the probability that at least 2 of them have the same birthday. e. How large a group is needed to give a 0.5 chance of at least two people having the same birthday?
Five men and five women line up at a checkout counter in a store. In how many ways can they line up if the first person in line is a woman and the people in line alternate woman, man, woman, man, and so on?
Company A pays \(\$ 23,000\) yearly with raises of \(\$ 1200\) per year. Company B pays \(\$ 26,000\) yearly with raises of \(\$ 800\) per year. Which company will pay more in year \(10 ?\) How much more?
Exercises will help you prepare for the material covered in the next section. In Exercises \(112-113,\) show that $$ 1+2+3+\cdots+n-\frac{n(n+1)}{2} $$is true for the given value of \(n .\) $$n-3: \text { Show that } 1+2+3-\frac{3(3+1)}{2}.$$
Make Sense? In Exercises \(78-81,\) determine whether each statement makes sense or does not make sense, and explain your reasoning. Beginning at 6: 45 A.M.., a bus stops on my block every 23 minutes, so 1 used the formula for the \(n\) th term of an arithmetic sequence to describe the stopping time for the \(n\) th bus of the day.
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