6 In a shipment of 12 air conditioners there are 3 with defe

6)         In a shipment of 12 air conditioners, there are 3 with defective thermostats. Two air conditioners will be selected at random and inspected one after the other. Find the probability that

a)         The second air conditioner is defective

b)         Exactly one is defective

Solution

X - no of defective thermostats

p = 0.25

X follows a Binomial distribution

n =2

a) P(first one good and second not good) = 0.75(0.25) = 0.1875

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b) P(X=1) = 2C1(0.25)(0.75) = 0.3750