RST Company has production facilities in Salt Lake City and Cleveland. The probability that in any given year a fire will damage the production facility in Salt Lake City is 5 percent. The probability that in any given year a fire will damage the Cleveland production facility is 4 percent. What is the probability that none of the production facilities will be damaged by fire in any given year

99.91%.

Explanation:

For Salt Lake City, the probability that there will be fire damage is:

5% = 0.05

Therefore, the probability that there will be no fire is:

99.95% = 0.9995

For Cleveland, the probability that there will be fire damage is:

4% = 0.04

Therefore, the probability that there will be no fire is:

99.96% = 0.9996

To calculate the probability that none of the production facilities will damaged by fire, we simply multiply both probabilities thus:

0.9995 X 0.9996

= 0.9991

The answer is therefore:

99.91%

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