Question

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.

Answer 1

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 = 25 C₄

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 p_i and x_i.

Following table represents the probability distribution of X :