Suppose that birthdays are equally likely to be on any day of the year (ignore February 29 as a possibility). Show 1.5, that the probability that two people chosen a; random have different birthdays is 364/365. Show that the probability that three people chosen at random all have different birthdays is
364/365 × 363/365
and extend this pattern to show that the probability that n people chosen at random all have different birthdays is
364/365 × ... × 366 - n/365
What then is the probability that in a group of n people, at least two people will share the same birthday? Evaluate this probability for n = 10, n = 15, n = 20, n = 25, n = 30 and n = 35. What is the smallest value of n for which the probability is larger than a half? Do you think that birthdays are equally likely to be on any day of the year?