Question 537176: A particular type of spring is manufactured by one of the two machines, A or B: 60% of the springs are made by machine A and the remainder by machine B. Of the springs manufactured, 3% are defective in some way, regardless of which machine made them. Find
a) the probability that a spring chosen at random is manufactured by machine A and is defective;
b) the probability that a spring chosen at random is manufactured by machine A or is defective.
c) Use a tree diagram as a relevant technique, to find the solution
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A particular type of spring is manufactured by one of the two machines, A or B: 60% of the springs are made by machine A and the remainder by machine B. Of the springs manufactured, 3% are defective in some way, regardless of which machine made them. Find
a) the probability that a spring chosen at random is manufactured by machine A and is defective;
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P(A and def) = P(def|A)*P(A) = 0.03*0.06 = 0.18
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b) the probability that a spring chosen at random is manufactured by machine A or is defective.
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P(A OR def) = P(A) + P(def) - P(A and def)
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= 0.6 + 0.03 - 0.18
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= 0.63-0.18
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= 0.45
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Cheers,
Stan H.
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