Problem 2: Fifteen parts are examined for defects. It is found that 10 are good,

Question

Problem 2: Fifteen parts are examined for defects. It is found that 10 are good, 3 have minor defects, and 2 have major defects. (a) What is the probability that a randomly selected one part is good? (b) Two parts are chosen at random from the 15 without replacement, that is, the first part chosen is not returned to the mix before the second part is chosen. Notice, then, that there will be only 14 possible choices for the second part. (i) What is the probability that both are good? (ii) What is the probability that exactly one part has a major defect? (You may use the tree diagram to find out all possible outcomes)

Explanation / Answer

a)P(selected one part is good)=10/15=2/3 (as there are 10 good parts out of 15)

b)

i)P(both are good)=P(first is good)*P(second good|first good)=(10/15)*(9/14)=3/7

ii)P(exactly one has major defect)=

=P(first not with major defect )*P(second with major defect|first not with major defect)+P(first with major defect)*P(second with major defect|first with major defect) =(13/15)*(2/14)+(2/15)*(13/14)=26/105

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