Answer:
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
[tex]\frac{1}{365}[/tex]
a) Probability that exactly 3 people have same birthday = [tex]\frac{1}{365^3}[/tex]
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 = [tex]\frac{1}{365^3}[/tex]
Expected value of days = np = [tex]\frac{1}{365^2}[/tex]
b) Distinct birthdays is binomail with p =1/365 and n = 365
Hence
expected value = np =1
