What is the chance that at least two people were born on the same day of the week if there are 3 people in the room?
I know how to get the answer which is 19/49 when considering all 3 people not being born on the same day. However, when I try to calculate the answer directly I seem to get it wrong.
Considering exactly 2 people being born on the same day I get 1*1/7*6/7. And then, exactly 3 people is 1*1/7*1/7. Thus, the total is 6/49 + 1/49 = 7/49. This must be something fairly simple, but I was just wondering where I'm going wrong.
Thanks
Best Answer
The only mistake you have committed is that you have not included the combinations while calculation of 2 were born on the same day If you name the persons A, B ,C Since the two of them may be A B, B C, C A Therefore you must also multiply it by a factor of 3