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From a lot containing 25 items, 5 of which are defective, 4 are chosen at random. Let X be the number of defectives found. Obtain the probability distribution of X if the items are chosen without replacement.

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Best answer

X represents the number of defective items drawn.

∴ X can take values 0, 1, 2 or 3

∵ there are total 25 items (20 good + 5 defectives) items

n(S) = total possible ways of selecting 5 items = 25C4

P(X = 0) = P(selecting no defective item)

P(X = 1) = P(selecting 1 defective item and 3 good items)

P(X = 2) = P(selecting 2 defective items and 2 good items)

P(X = 3) = P(selecting 3 defective items and 1 good item)

P(X = 4) = P(selecting 4 defective items and no good item)

Now we have pi and xi.

Following table represents probability distribution of X :

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