Problem
Answer the following questions about a family of six people, assuming that the birthdays are uniformly distributed through the days of a week, through the days of a month, through each month of a year, and through the 365 days of the year. Also assume that a year is exactly 365 days and each month is exactly 30 days.
a. What is the probability that two of the family members have the same birthday? What is the probability that none of them have the same birthday?
b. What is the probability that two of the family members are born in the same month? What is the probability that none of them were born in the same month?
c. What is the probability that one of the family members is born on the first day of a month?
d. What is the probability that three of the family members are born on the same day of the week?