Thread: Probability Mass Function

There are 89 students in your probability class. What is the probability that exactly one other student has the same birthday as you? (For simplicity, exclude birthdays on February 29.) Calculate this exactly using the binomial PMF and also approximately by using the Poisson PMF.

1. Exact answer:
2. Poisson approximation:

Originally Posted by essedra

There are 89 students in your probability class. What is the probability that exactly one other student has the same birthday as you? (For simplicity, exclude birthdays on February 29.) Calculate this exactly using the binomial PMF and also approximately by using the Poisson PMF.

1. Exact answer:
2. Poisson approximation:

Here is your starting point:

Let X be the number of students having your birthday.

X ~ Binomial(n = 89, p = 1/365).