Thread: Probability that of 3 people selected at random, at least 2 were born on the same day

What is the probability that, of three people selected at random, at least two were
born on the same day of the week?
I know the answer is 19/49 but how?

Originally Posted by sundance240

What is the probability that, of three people selected at random, at least two were
born on the same day of the week?
I know the answer is 19/49 but how?

The back door method.
(7/7)(6/7)(5/7) is the probability they were all born on different days of the week.
Subtract that from 1. What do you get? WHY?

Chance of at least two were born on the same day of the week = 1 - Chance of all three born on different days of the week

Chance of three random people born on different days of the week = 1 * 6/7 * 5/7 = 30/49

Chance of at least two were born on the same day of the week = 1 - 30/49 = 19/49

Sorry for re-post, didn't see the above reply

I believe this is also called the birthday paradox. Birthday problem - Wikipedia, the free encyclopedia