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'm wondering if my solution is accurate, as my answer was different than the solution I found:
Probability that there are at least 2 people in the room born on the same day = 1 - (No one was born on the same day) - (Exactly one person was born on the same day)
There are (3 choose 2) different pairs of couples. Each couple has the same birthday as another couple with the chances of 1/7 and different with chances 6/7. Thus:
$$1 – (6/7)^3 – 3(1/7)(6/7)^2 = 0.0553$$
Thanks for any help!