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

• Apr 16th 2011, 11:34 AM
sundance240
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?
• Apr 16th 2011, 11:45 AM
Plato
Quote:

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?
• Apr 16th 2011, 11:45 AM
yyhow
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
• Apr 17th 2011, 10:56 AM
Sherrie
I believe this is also called the birthday paradox. Birthday problem - Wikipedia, the free encyclopedia