00:01
In this problem, we need to determine how many people are needed so that the probability that at least one of them has the same birthday than you, birthday as you is greater than half.
00:11
So let us assume that there are a total of n people, that we require n people.
00:18
Now, the probability that one person does not have the same birthday as you will be 364 divided by 365.
00:29
The reason is that you have one birthday and other than that day, there will be 364 days in a year.
00:37
So that will be the number of favorable outcomes, the 364 days of the year apart from the day which is your birthday.
00:44
And the total number of outcomes is all the days in the year.
00:48
So 365.
00:49
So the probability that one person does not have the same birthday as you is 364 by 365.
00:54
So the probability that all n people do not have the same birthday as you will be obtained by multiplying this probability n times.
01:09
So we just have to multiply it n times using the multiplication rule of probability.
01:16
So this will be 364 by 365 to the power n.
01:22
So this is the probability that none of these n people have the same birthday as you.
01:30
So the probability that at least one of them has the same birthday as you will be one minus this probability because the event of at least one of them having the same birthday as you is the complementary event of the event of none of them having the same birthday as you.
01:48
So we get this as a required probability and we want this to be.
01:52
Greater than half.
01:55
So this needs to be greater than half...