It is somewhat surprising to learn the probability that 2 persons in a class share the same birthday. As an approximation, assume that the 365 days are equally likely birthdays.
(a) What is the probability that, among 3 persons, at least 2 have the same birthday? [The reasoning associated with a tree diagram shows that there are 365 × 365 × 365 possible birthday outcomes. Of these, 365 × 364 × 363 correspond to no common birthday.)
(b) Generalize the above reasoning to N persons. Show that

We see that with N = 23 persons, the probability is greater than 1/2 that at least two share common birthday.)

Transcribed Image Text:

P[ No common birthday ] 365 x 364 x . . . x (365-N + 1) (365) Some numerical values are 5 9 18 22 23 P[ No common 973 905 .653 .524 .493 birthday ]