Suppose that there are 32 people in your statistics class and you are divided into 16 teams of 2 students each. You happen to mention that your birthday was last week, upon which you discover that your teammate's mother has the same birthday you have (month and day, not necessarily year). Assume that the probability is 1/ 365 for any given day.

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Suppose that there are 32 people In your statistlu class and you are divided into 16 teams of 2 students each. You happen to mention that your birthday was last week, upon which you disoover that your teammate's mother has the same birthday you have (month and day, not necessarily year). Assume that the probability ls % for any given day. (a) What is the probability that your teammate's mother would have the same birthday as yours? (Round your answer to four decimal places.) :| (b) Suppose that your teammate has two siblings and two parenm, for a family of size five. What is the probability that at least one of your teammate's family (including your teammate) has the same birthday as yours' assuming their birth dates are all independent? (Round your answer to four decimal places.) :| {c} Is the fact that you share a birthday with one of your classmates' family members a surprising coincidence? Explain. (Round your answer to four decimal places.) , if we suppose that each person in the class other than you has two parents and two siblings, then the probability that you share a birthday with at least one of your classmates' family members (including your classmates) Is I: .

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