A hatch of 200 samples of containers for frozen apple juice contains 20 that are

Question

A hatch of 200 samples of containers for frozen apple juice contains 20 that are defective. Three samples are selected at random, without replacement from the batch. Identify the sample space S for this experiment. What is the probability that the first one selected is not defective and the second and third samples are defective? What is the probability that the second one selected is not defective given that the first one was defective? What is the probability that the second and third samples are defective knowing that the first one is defective? What is the probability that all three are defective? What is the probability that all three are acceptable?

Explanation / Answer

A) Let D denote defective and N denote non defective, then, th sample space S is {DDD, DDN, DND, NDD, DNN, NDN, NND, NNN}

B) P(NDD) = (190/200)x(10/199)x(9/198) = 0.0022

c) If first one was defective, there are 190 not defective ones remaining and hence P(2nd one not defective) = 190/199

d) If first one was defective, there are 9 defective in the remaining 199. P(2nd and 3rd defective) = (9/199)x(8/198) = 0.0018

e) P(all 3 are defective) = (10/200)x(9/199)x(8/198) = 0.00009

f) P(all 3 are acceptable) = (190/200)x(189/199)x(188/198) = 0.8567

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