Question

Forty-four people have served as President of the United States. Grover Cleveland is often counted twice because he served two non-consecutive terms. Assume there are 366 days in a year, and assume you are a Bayesian.

a. What is the probability that at least two of these 44 Presidents share the same birthday? (Same day and month, though not necessarily the same year.)

b. What is the probability that at least one of these Presidents shares your birthday?

Answer 1

Each of the 44 President can select their n=birthday in 366 ways so possible number of ways 44 president can have their birthday is

(a)

The number of each of 44 president have different birthday is

The probability that all president have different birthday is

So the probability that at least two of these 44 Presidents share the same birthday is

Answer: 0.9324

(b)

There are 365 days excluding your birthday. So number of ways in which no president share your birthday is

The probability that no president share your birthday is

So the probability that at least one of these Presidents shares your birthday is

Answer: 0.1134