An independent research group has been studying the chances that an accident at a nuclear power plant will result in radiation leakage. The group considers that the only possible types of accidents at a reactor are fire, mechanical failure, and human error, and that two or more accidents never occur together. It has performed studies that indicate that if there were a fire, a radiation leak would occur 20 percent of the time; if there were a mechanical failure, a radiation leak would occur 50 percent of the time; and if there were a human error, a radiation leak would occur 10 percent of the time. Its studies have also shown that the probability of A fire and a radiation leak occurring together is 0.0010. A mechanical failure and a radiation leak occurring together is 0.0015. A human error and a radiation leak occurring together is 0.0012. What are the respective probabilities that a radiation leak was caused by a (a) fire, (b) mechanical failure, and (c) human error?

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Chapter1: Combinatorial Analysis
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An independent research group has been studying the chances that an accident at a
nuclear power plant will result in radiation leakage. The group considers that the only
possible types of accidents at a reactor are fire, mechanical failure, and human error,
and that two or more accidents never occur together. It has performed studies that
indicate that if there were a fire, a radiation leak would occur 20 percent of the time; if
there were a mechanical failure, a radiation leak would occur 50 percent of the time;
and if there were a human error, a radiation leak would occur 10 percent of the time. Its
studies have also shown that the probability of
A fire and a radiation leak occurring together is 0.0010.
A mechanical failure and a radiation leak occurring together is 0.0015.
A human error and a radiation leak occurring together is 0.0012.
What are the respective probabilities that a radiation leak was caused by a (a) fire, (b)
mechanical failure, and (c) human error?
Transcribed Image Text:An independent research group has been studying the chances that an accident at a nuclear power plant will result in radiation leakage. The group considers that the only possible types of accidents at a reactor are fire, mechanical failure, and human error, and that two or more accidents never occur together. It has performed studies that indicate that if there were a fire, a radiation leak would occur 20 percent of the time; if there were a mechanical failure, a radiation leak would occur 50 percent of the time; and if there were a human error, a radiation leak would occur 10 percent of the time. Its studies have also shown that the probability of A fire and a radiation leak occurring together is 0.0010. A mechanical failure and a radiation leak occurring together is 0.0015. A human error and a radiation leak occurring together is 0.0012. What are the respective probabilities that a radiation leak was caused by a (a) fire, (b) mechanical failure, and (c) human error?
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