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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