Answer to Question #295207 in Statistics and Probability for love

Question

A shipment of 25 similar laptop computers to a retail outlet contains 5 that are defective. If a school makes a random purchase of 3 of these computers, find the probability when the school accidentally purchased 1 defective and 2 are nondefective computers? Convert your answer in decimals with three (3) significant figures.

Answer 1

Let $D$ be the event that a laptop is defective. $D'$ is the event that a laptop is not defective.

The probability that a laptop is defective is, $p(D)={5\over25}$ and $p(D')=1-p(D)=1-{5\over25}={20\over25}$

The probability that a school purchases 1 defective and 2 non-defective laptops is,

$({5\over25}\times{20\over24}\times{19\over23})+({20\over25}\times{5\over24}\times{19\over23})+({20\over25}\times{19\over24}\times{5\over23})=0.413$