# 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?

Mar 16, 2018

approx 61.5%

#### Explanation:

The probability that a laptop is defective is $\left(\frac{6}{22}\right)$
The probability of a laptop not being defective is $\left(\frac{16}{22}\right)$

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.

$P \left(X = 1\right)$ = (3 choose 1) ${\left(\frac{6}{22}\right)}^{1} \times {\left(\frac{16}{22}\right)}^{2} = 0.43275$

$P \left(X = 2\right)$= (3 choose 2) ${\left(\frac{6}{22}\right)}^{2} \times {\left(\frac{16}{22}\right)}^{1} = 0.16228$

$P \left(X = 3\right)$=(3 choose 3) ${\left(\frac{6}{22}\right)}^{3} = 0.02028$

(Sum up all of the probabilities)

$= 0.61531 \approx 0.615$

Mar 16, 2018

0.6364