Question

A lot contains 12 items and 4 are defective. If two items are drawn at random from the lot, without replacement, what is the probability there is exactly one defective?

Answer 1

Number of items in the lot = 12

Number of defective items of the lot =4

Number of items drawn from the lot =2

Number of ways drawing 2 items from 12 items =

Number of ways of drawing 1 defective item from 4 defective items =

Number of ways of drawing 1 non defective item from 8 non defective items =

Probability there is exactly one defective =

(Number of ways of drawing 1 defective item from 4 defective items x Number of ways of drawing 1 non defective item from 8 non defective items) / Number of ways drawing 2 items from 12 items

= (4x8)/66 = 32/66 = 16/33 = 0.4848

Probability there is exactly one defective = 0.4848