Question: Problem 2.28 Consider the following variation on Fellers birthday problem (Example 2.24). The martian year is 669 days long. (a) There are k martians in

Problem 2.28 Consider the following variation on Feller’s birthday problem (Example 2.24). The martian year is 669 days long.

(a) There are k martians in a room; derive a formula for the probability that at least two martians in the room have a common birthday.

(b) Use your answer to part

(a) to show that when k ≥ 31 the probability that at least two martians in the room have a common birthday is 0.506.

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