Data Management (MDM4U) · Probability Distributions

Hypergeometric probability distribution

Compute probabilities for sampling without replacement using the hypergeometric distribution. Unlimited questions, five difficulty levels, and a full worked solution every time, included free with weekly lessons.

Practice this skill Curriculum: MDM4U-PD1.2

Try one

A deck contains 10 cards, of which 4 are face cards (the rest are non-face cards). If you randomly select 3 cards without replacement, what is the probability that exactly 3 of them are face cards?

N = 10, K (successes) = 4, n (sample size) = 3, k = 3

Answer: 1/30

See one solved, step by step

A batch contains 13 circuit boards, of which 6 are defective circuit boards (the rest are working circuit boards). If you randomly select 4 circuit boards without replacement, what is the probability that exactly 1 of them are defective circuit boards?

N = 13, K (successes) = 6, n (sample size) = 4, k = 1

📘 Worked solution

1Ways to choose 1 of the 6 defective circuit boards: C(6, 1) = 6.Pick the successes from the group that has them.

2Ways to choose 3 of the 7 working circuit boards: C(7, 3) = 35.The rest of the sample must come from the remaining items.

3Total ways to choose 4 from all 13: C(13, 4) = 715.This is the whole sample space, ignoring which items are successes.

4P = (6 · 35) / 715 = 210715 = 42143Multiply the two favourable counts together, divide by the total, and reduce.

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