Question

Check if the chance that at least two people in our class (n=66) have the same birthday (MM/DD) is very unlikely or very likely?

Answer 1

Answer)

Probability that at least 2 people have the same birthday

= 1 - probability that no one have the same birthday

Probability (no one having same birthday)

First person can have any birthday among 365 days

= 365/365

For second person we have only 364 days as he or she cannot have the same as that of first

= 364/365 and so on

So we have = (365*364........*300)/(365^66)

P(at least 2 person have the same birthday) = 1 - [(365*364....*300)/(365^66)]

= 0.99809570464

As the probability is huge

It is very likely