Thread: Simple Probability Question

Find the probability that in a group of 10
people, all born in April, at least two have the same birthday.


I thought of calculating the probability that no two people have the same birthday.

April has 30 days, so

1. person has 30/30 chance
2. person has 29/30 chance
3. person has 28/30 chance
...
10. person has 21/30 chance
to have a different birthday as the others.

Then I get 29/30*28/30*...*21/30 = 0.185, which means there is a
1 - 0.185 = 0.815 probability that 2 persons have the same birthday.

I think thats too high, but thats all i can say.

Hello EinStone

Originally Posted by EinStone

Find the probability that in a group of 10
people, all born in April, at least two have the same birthday.


I thought of calculating the probability that no two people have the same birthday.

April has 30 days, so

1. person has 30/30 chance
2. person has 29/30 chance
3. person has 28/30 chance
...
10. person has 21/30 chance
to have a different birthday as the others.

Then I get 29/30*28/30*...*21/30 = 0.185, which means there is a
1 - 0.185 = 0.815 probability that 2 persons have the same birthday.

I think thats too high, but thats all i can say.

No, your reasoning and answer are perfect!

It does seem unlikely, but then so does this: Assuming all months are the same length and that birthdays are randomly distributed throughout the year, did you know that the odds that, in a group of 5 people, at least two will have birthdays in the same month are nearly 2:1 in favour? (In fact, it's 89:55.) Use the same method to work it out. Surprising, isn't it?

Grandad