What is the probability that only one of the items is defective?

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container

1 Answer
Feb 5, 2018

Probability of getting only one defective item from the two

containers is #color(red)(19/40)#

Explanation:

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Container 1 Total items = 8, defective = 3

Container 2 Total items = 5, defective = 2

Probability of getting 1 defective item in container 1 = 3/8

Probability of getting no defective item in container 1 = 5/8

Probability of getting 1 defective item in container 2 = 2/5

Probability of getting no defective item in container 2 = 3/5

When a defective item is selected from container 1, we should not pick a defective one from container 2 and vice versa.

Probability of getting only one defective item is

#=( 3/8 * 3/5) + (5/8 * 2/5) = 9/40 + 10/40 = 19/40#