Consider a group of n say n 1000 chips Each chip in the gro

Consider a group of n (say n > 1000) chips. Each chip in the group can be either good or bad. Assume that each of the chips is good with probability 2/5.

(a) Find the probability that the number of good chips is greater than 4 and less than 8.

(b) Find the expected value of the number of good chips

(c) Four chips are selected at random. Compute the probability that exactly three of the selected chips are bad.

Solution

Let x be the no of good chips. X is a binomial variate with p =0.4 and n > 1000

a) the probability that the number of good chips is greater than 4 and less than 8.=

P(4<x<8) =cum prob of 7-cum prob of 4 = 1.156x10^-212 and prob for 8 =1.349x10^-204

Hence answer is 1.349x10^-204-1.156x10^-212 = 1.349x10^-204 appxy.

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b) Expected value = np >400

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c) 3 out of 4 are bad implies only 1 is good out of 4.

Prob ( 1 is good in 4) = 0.3456