silemus.
← All examples
  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

16Two cards both aces

Two cards are drawn without replacement from a standard 52-card deck. Find P(both are aces)\displaystyle P(\text{both are aces}).

Because the cards aren't replaced, multiply dependent probabilities: 4/52 for the first ace, then 3/51 for the second. That gives (4/52)(3/51) = 1/221, confirmed by 4C2/52C2 = 6/1326 = 1/221.

How good is this answer?