For a group of 100 people, compute(a) the expected number of days of the year that are birthdays of exactly 3 people.(b) the expected number of distinct birthdays.

Step-by-step explanation:

Leaving leap years, a year contains 365 days.

For a group of 100 people, each person is independent of the other and probability of any day being his birthday has a chance of

a) Probability that  exactly 3 people have same birthday =

Each day is independent of the other

And hence no of days having exactly 3 persons birthday out of 100 persons is binomial with n = 365 and p =

Expected value of days = np =

b) Distinct birthdays is binomail with p =1/365 and n = 365

Hence

expected value = np =1

dunno

step-by-step explanation: