Q14 of 77 Page 32

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 :



More from this chapter

All 77 →
12

Two dice are thrown together, and the number appearing on them noted. X denotes the sum of the two numbers. Assuming that all the 36 outcomes are equally likely, what is the probability distribution of X?

 13

A class has 15 students whose ages are 14, 17, 15, 14, 21, 19, 20, 16, 18, 17, 20, 17, 16, 19 and 20 years respectively. One student is selected in such a manner that each has the same chance of being selected and the age X of the selected student is recorded. What is the probability distribution of the random variable X?

 15

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.

 16

Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Find the probability distribution of the number of kings.