Three people are asked on which day of the week they were born. Suppose that bir

Question

Three people are asked on which day of the week they were born. Suppose that birth rates are equal for all days of the week. Let X be the number of different days of the week that are named by the three respondents. (So, for instance, if two were born on a Monday, and one on Friday, then X = 2). What is the probability function for X? Suppose that you keep asking people which day of the week they were born until you have identified three people who were born on different days. What is the expected number of people you need to ask to find three such people? Now suppose birth rates are not equal, and in particular for any baby the probability of being born on one of the weekdays (Monday to Friday) is 2/12. whereas the probability of being born on Saturday or Sunday is 1/12 each. What is the probability now that three people are all born on a different day? Suppose that a week had n days instead of seven days, and each person is equally likely to be born on each of the n days. If you sample k people, what is the probability t hey are all born on different days?

Explanation / Answer

solution:

if X is less than 2 then probability = 0

if X is equal to 2 then probability = 1

if x is more than 2 then probability =1

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