From a lot of 10 bulbs, which includes 3 detectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.

X represents the number of defective bulbs drawn.


∴ X can take values 0,1 or 2 (as maximum bulbs drawn are 2)


∵ there are total 10 bulbs (7 good+3 defectives)


n(S) = total possible ways of selecting 2 items from sample =


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


P(X = 1) = P(selecting 1 defective bulb and 1 good bulb)


=


P(X = 1) = P(selecting 0 defective bulb and 2 good bulb)


=


Now we have pi and xi.


Following table represents the probability distribution of X :



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