Five defective bolts are accidentally mixed twenty good ones. If four bolts are drawn at random from this lot, find the probability distribution of the number of defective bolts.

X represents the number of defective bolts drawn.


∴ X can take values 0,1,2 or 3


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


n(S) = total possible ways of selecting 5 bolts =


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


P(X = 1) = P(selecting 1 defective bolt and 3 good bolts)


=


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


=


P(X = 3) = P(selecting 3 defective bolts and 1 good bolt)


=


P(X = 4) = P(selecting 4 defective bolts and no good bolt)


=


Now we have pi and xi.


Following table represents the probability distribution of X :



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