An interesting problem from probability is the birthday problem. The problem deals with determining the likelihood that at least two people share the same birthday in a room of n individuals. Open the data file, which represents simulated birthdates of 15 individuals 2000 times. Each birthdate was assigned a number from 1 (January 1) to 365 (December 31). Complete parts (a) through (c) below.
Added by Kevin M.
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Step 1: Open the data file and read the birthdates of the 15 individuals for each of the 2000 simulations. Show more…
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Problem 50. The birthday problem. Consider n people who are attending a party. We assume that every person has an equal probability of being born on any day during the year, independent of everyone else, and ignore the additional complication presented by leap years (i.e., assume that nobody is born on February 29). What is the probability that each person has a distinct birthday?
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The birthday problem What’s the probability that in a randomly selected group of 30 unrelated people, at least two have the same birthday? Let’s make two assumptions to simplify the problem. First, well ignore the possibility of a February 29 birthday. Second, we assume that a randomly chosen person is equally likely to be born on each of the remaining 365 days of the year. (a) How would you use random digits to imitate one repetition of the process? What variable would you measure? (b) Use technology to perform 5 repetitions. Record the outcome of each repetition. (c) Would you be surprised to learn that the theoretical probability is 0.71? Why or why not?
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