A collection of 22 laptops includes 6 defective laptops. If a sample of 3 laptops is randomly chosen from the collection, what is the probability that at least one laptop in the sample will be defective?

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Answer 1 · 2018-03-16T16:41:25

$approx 61.5%$

The probability that a laptop is defective is $(6/22)$
The probability of a laptop not being defective is $(16/22)$

The probability that at least one laptop is defective is given by:

P(1 defective)+P(2 defective)+P(3 defective)

, as this probability is cumulative. Let $X$ be the number of laptops found to be defective.

$P(X=1)$ = (3 choose 1) $(6/22)^1 times (16/22)^2=0.43275$

$P(X=2)$ = (3 choose 2) $(6/22)^2 times (16/22)^1=0.16228$

$P(X=3)$ =(3 choose 3) $(6/22)^3=0.02028$

(Sum up all of the probabilities)

$=0.61531 approx 0.615$

Answer 2 · 2018-03-16T19:35:00

0.6364

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