Question

in a classroom there are 30 student what is the probability that two of them have the same birthday on the same date

Answer 1

So here it is: a special math problem for a special little girl. Someday you’ll know all the math to understand this post (trust me, I’ll make sure of it!).

The Birthday Problem in Real Life

The first time I heard this problem, I was sitting in a 300 level Mathematical Statistics course in a small university in the pacific northwest. It was a class of about 30 students and the professor bet that at least two of us shared the same birthday.

He then proceeded to have everyone state their birthday. When it came to my turn I stated my birthdate as “two cubed, three cubed,” which made the class laugh as our cerebral professor took awhile to decipher the date.

Anyway like he predicted before he got to the last student a pair of matching birthdays had been found.

So how lucky was it that he found a matching pair?

Warm Up

Assumption: for the sake of simplicity we’ll ignore the possibility of being born on Feb. 29th.

Let’s begin with a simple example to warm up our brains:

What is the probability that two people share the same birthday?

Person A can be born on any day of the year since they’re the first person we’re asking. The probability of being born any day of the year is 1 or more specifically: 365/365.

Since Person B must be born on the same day as Person A their probability is 1/365.

We want both of these events to happen so multiply the probabilities:

Answer 2

favourable outcome=2
total outcome=30
probability=favourable outcome/total outcome
=2/30
=1/15