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

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SUMMARY

The probability of at least one person being born on a specific birthday among four randomly selected individuals is calculated using the formula 1 - (364/365)^4. This results in a probability of approximately 0.02, indicating a 2% chance that at least one of the four shares the same birthday. The initial miscalculation using (1/365)^4 incorrectly represented the scenario, as it only accounted for the probability that all four individuals share the same birthday. Understanding the complementary probability is crucial for accurate calculations in this context.

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  • Basic understanding of probability theory
  • Familiarity with complementary probability concepts
  • Knowledge of the birthday problem in statistics
  • Ability to perform exponentiation and basic arithmetic calculations
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  • Study the birthday problem in probability theory
  • Learn about complementary probability and its applications
  • Explore advanced probability concepts, such as binomial distributions
  • Practice calculating probabilities with different sample sizes
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Students studying probability, educators teaching statistics, and anyone interested in understanding the mathematics behind birthday coincidences.

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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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