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

51Hypergeometric probability

A box has 10 items, 3 of them defective. 4 are chosen at random without replacement. Find P(exactly 1 is defective)\displaystyle P(\text{exactly 1 is defective}).

Use the hypergeometric setup: choose 1 defective from 3, and 3 good ones from 7, divided by all ways to choose 4 from 10. That gives C(3,1)·C(7,3)/C(10,4) = 105/210 = 1/2.

How good is this answer?