What is the Probability of Selecting Someone Born on My Birthday?

[jimmyjamz]

I have a question regarding a probability question. If four people are randomly selected what is the probability that at least one is born on my birthday. This would make me think that I want to do the formula of

1 - (1/365)^4 which comes out to be
1 - .000000000005636405776 = .999999999 which just doesn't seem right to me.

I also have to do what is the probability that one is born on my birthday which makes me think that I want to do (1/365)^4

Am I anywhere near the right path?

 

[HallsofIvy]

(1/365)⁴ is the probability that all 4 were born on your birthday. 1- (1/365)⁴ is the probability that at least one was NOT born on your birthday.

The probability that a given person was NOT born on your birth day is 364/365 (disregarding leap year). The probability that out of four people NONE of them was born on your birthday is (364/365)⁴ so the probability that at least one was born on your birthday is 1- (365/365)⁴. That's about 0.02.

 

[jimmyjamz]

Thank you very much. That explanation cleared things up tremendously. It's an extremely easy concept but for some reason I'm having issues grasping it. Thanks again!