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Business Mathematics I
Homework 6
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Math 115a, Section:
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1. Box I contains three black balls and two white balls. Box II contains one black ball
and three white balls. A person chooses one of the boxes at random, and then draws one
of the balls in that box. Let I be the events that the ball is drawn from Box I, let II be the
event that the ball is drawn from Box II, let B be the event that the selected ball is black,
and let W be the event that the selected ball is white. Compute P ( I | W ) and P ( I | B ) .
Solution.
2. Box I contains three black balls and two white balls. Box II contains one black ball
and three white balls. A person chooses one of the boxes at random, and then draws one
of the balls in that box. Let I be the events that the ball is drawn from Box I, let II be the
event that the ball is drawn from Box II, let B be the event that the selected ball is black,
and let W be the event that the selected ball is white. Compute P( II | W ) and P ( II | B) .
Solution.
3. The probability that a defective part is produced by a certain machine depends on the
condition of the machine. If the machine is in good condition, then the probability of a
defective part is 0.02. If it is in fair condition, then the probability of a defective part is
0.10. If it is in poor condition, then the probability of a defective part is 0.3. The
probability that the machine is in good condition is 0.8, the probability that it is in fair
condition is 0.1, and the probability that it is in poor condition is 0.05. If a defective part
is found, what is the probability that it was produced while the machine was in good
condition?
Solution.
4. The probability that a defective part is produced by a certain machine depends on the
condition of the machine. If the machine is in good condition, then the probability of a
defective part is 0.02. If it is in fair condition, then the probability of a defective part is
0.10. If it is in poor condition, then the probability of a defective part is 0.3. The
probability that the machine is in good condition is 0.8, the probability that it is in fair
condition is 0.1, and the probability that it is in poor condition is 0.05. If a defective part
is found, what is the probability that it was produced while the machine was in poor
condition?
Solution.