Is pk 1 pk365-k365 and if so why? find the smallest class, Ask an Expert

Statistics

In a class of K students, no one was born on February 29th, and no one is related to anyone else. Denote as P(K) the probability that these K students have K different birthdays.

(a) Is P(K + 1) = P(K)(365-K)/365 and, If so, why?
(b) Find the smallest class size K for which the probability that two or more students have the same birthday exceeds 0.5.
(c)In part (a), did you use the fact that no one is related to anyone else?
(d) Adapt the formula in part (a) and redo part (b) for the case of a grammer school in which twins, if any, are put in the same class. Suppose that each preganancy produces twins (who have the same birthday) with probability of 1/84.

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