A technician is assigned the task of examining transistors before they are insta

Question

A technician is assigned the task of examining transistors before they are installed into a radio. She has a box containing 12 transistors, 3 of which are defective.

(a) Suppose 2 transistors are randomly selected with replacement. Find the probability that both are defective (i.e. find P(D1 and D2)). Assume independence.

(b) Suppose 2 transistors are randomly selected with replacement. Find the probability that the first is defective or the second is defective, i.e. find P(D1 or D2).

(c) Suppose 2 transistors are randomly selected without replacement. Given that the first transistor is defective, determine the probability that the second transistor is defective (i.e. find P(D2D1)).

(d) Suppose 2 transistors are randomly selected without replacement. Find the probability that both are defective (i.e. find P(D1 and D2)).

(e) Suppose 2 transistors are randomly selected without replacement. Find the probability that the first is defective or the second is defective, i.e. find P(D1 or D2). Hint: Use the law of total probability to find P(D2).

Explanation / Answer

12 transistor 3 defective

a) probability both are defective (with replacement) = (3/12)^2 = 1/16

b) probability either one is defective (with replacement) = 1 - probability that both are not defective

= 1 - (9/12)^2

= 1 - 0.75^2

= 0.4375

c) P(D2|D1) = 2/11   {as there are 2 defective item left out of 11}

d)

without replacement

probability both are defective = 3C2 / 12C2 = 3*2 /(12*11) = 1/22

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