Consider the experiment, called the birthday problem , where our task is to determine the probability that in a group of people of a certain size there are at least two people who have the same birthday (the same month and day of month). suppose there is a room with 9 people in it, find the probability that at least two people have the same birthday. ignore leap years; assume each year has 365 days.

There is a 0.02% probability that at least two people have the same birthday.

Step-by-step explanation:

There are only two possible outcomes: Either the people do have the same birthday or they do not. So we use the binomial probability distribution.

Binomial probability

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And is the probability of X happening.

In this problem, we have that:

There are 365 days in a year, so the probability that a person has a birthdday on any given day is given by .

Suppose there is a room with 9 people in it, find the probability that at least two people have the same birthday.

There are 9 people, so .

We also want to find

And

We also have that:

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There is a 0.02% probability that at least two people have the same birthday.