Finite Question

Question

Find the probability that in a group of 4 people, at least two were born in the same month. You may assume that each month is equally likely. Give the answer to 3 decimal places.

Answer 1

Hi Cassie, 

 

There are 12 ways to say the month that the first person was born in.  There are also 12 choices for the month that person 2 could be born in.  There are likewise 12 choices for person 3 and 12 choices for person 4.

 

The total number of ways that we could name the months that 4 people are born in would be 12*12*12*12 = 20736

 

If we wanted to list out all of the ways for 4 people to not share a birth month, then they would all have to have different birth months, so we'd have 12 choices for the first person, but only 11 for the second, then 10 for the third, and then 9 for the fourth.  So the total number of ways they would not share a birth month would be 12*11*10*9 = 11880.

 

If at least 2 of them did share a birth month (what your problem is asking for), then there would be 20736 - 11880 ways to do that.  20736 - 11880 = 8856

 

So the probability that at least two of them share a birth month would be 8856 / 20736 = 0.427

 

Hope that helps!

 

Jeff