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

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The probability of at least one person among four randomly selected individuals being born on a specific birthday can be calculated using the formula 1 - (364/365)^4. This indicates that the chance of none of the four sharing the birthday is (364/365)^4, leading to a probability of about 0.02 for at least one match. The initial approach of using (1/365)^4 was incorrect, as it represented the probability that all four share the same birthday. Understanding the distinction between these probabilities clarified the concept significantly for the participants. Overall, the discussion highlights the importance of correctly applying probability formulas in birthday-related scenarios.
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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?
 
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(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.
 
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!
 

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