silemus.
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  1. 14Arrangements with repeats
  2. 16Two cards both aces
  3. 18Birthday paradox, 23 people
  4. 21Bayes' theorem on disease test
  5. 22Bayes' theorem on urns
  6. 23Total probability, defective part
  7. 34Finding cc for a density
  8. 35Expected value of XX
  9. 41Sampling distribution of mean
  10. 4295% CI for the mean
  11. 45Covariance from E[XY]
  12. 46Correlation from covariance
  13. 48zz test statistic
  14. 50Stationary distribution, 2 states
  15. 51Hypergeometric probability

18Birthday paradox, 23 people

23 people are in a room; birthdays are uniform over 365 days (no leap years). Find P(at least two share a birthday)\displaystyle P(\text{at least two share a birthday}). Give the answer to 4 decimal places.

It's easier to compute the chance everyone has a different birthday, then subtract from 1. Multiplying 365/365 × 364/365 × ... × 343/365 (23 terms) gives about 0.4927, so P(share) = 1 − 0.4927 ≈ 0.5073.

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