A factory contains 20 machines and it is known that 3 of those machines are defe

Question

A factory contains 20 machines and it is known that 3 of those machines are defective. (a) Two machines are selected, at random, without replacement, from the lot. Determine the probability that the second machine selected is defective. (b) Two machines are selected, at random, without replacement, from the lot. Determine the probability that exactly 2 machines are defective. (c) What is the probability that the second machine selected is defective given that the first machine was not defective?

Explanation / Answer

a)P(2nd machine is defective)=P(first machine is good and second is defective+first machine is defective and second is defective) =(17/20)*(3/19)+(3/20)*(2/19)=3/20 =0.15

b)

P(exactly two machines are defective)=P(first machine is defective and second is defective)

=(3/20)*(2/19)=3/190 =0.0158

c)

P(second machine defective|first machine good)

=P(first machine is good and second is defective)/P(first machine is good) =(17/20)*(3/19)/(17/20)=3/19

=0.1579

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