Skip to main content

Hypergeometric: 3 batteries from 24

Short answer

Use hypergeometric distribution: (a) 0.4032, (b) 0.4536, (c) 0.1433.

A quality control engineers inspects a random sample of 3 batteries from each lot of 24 car batteries that is ready to shipment. If such a lot contain six batteries with slight defects, what is the probabilities that the inspector's sample will contain a) None of the batteries with defect b) Only one of the batteries with defect c) At least two of the batteries with defect

Lot size N = 24, defective K = 6, good = 18, sample n = 3 drawn without replacement, so X (number of defectives in the sample) is hypergeometric:

P(X = x) = C(6, x) · C(18, 3 − x) / C(24, 3), where C(24, 3) = 2024.

x   C(6,x)·C(18,3-x)      P(X = x)
0   1 × 816   = 816       0.4032
1   6 × 153   = 918       0.4536
2   15 × 18   = 270       0.1334
3   20 × 1    = 20        0.0099

a) None defective

P(X = 0) = 816 / 2024 = 0.4032

b) Only one defective

P(X = 1) = 918 / 2024 = 0.4536

c) At least two defective

P(X ≥ 2) = P(2) + P(3) = (270 + 20) / 2024 = 290 / 2024 = 0.1433

(Check: 1 − 0.4032 − 0.4536 = 0.1432, the same up to rounding.)

Answer: (a) 0.4032, (b) 0.4536, (c) 0.1433

✓ Answer checked by Claude Sonnet 5.5

Related questions

All Probability and Statistics chapter 2 questions →