Birthday Problem: Find the Probability of 3 People Sharing the Same Birthday

[skip_it2]

Three people are selected at random. Find the probability that

(a) all three share the same birthday:

(365/365)(1/365)(1/365) = 0.00000751

(b) none of the three shares the same birthday. Assume 365 days in a year.

(365/365)(364/365)(363/365) = 0.992

 

[statdad]

Sorry - I was thinking this was a homework forum problem - is it homework?
Try a direct counting approach:
1) Figure out how many possibilities there are for birthdays for the three (no restrictions)
2) For 'a', count the number of ways all three could have the same birthday, then divide by the answer to '1'
3) For 'b', count the number of ways none have the same birthday, then divide by the answer to '1'

Thanks for adding your work. It wasn't here before.

 

[mXSCNT]

Your answers are correct.