1. In a certain city, the probability that an automobile willbe stolen and found
ID: 2953829 • Letter: 1
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1. In a certain city, the probability that an automobile willbe stolen and found within one week is 0.0009. The probability thatan automobile will be stolen is 0.0015. Find the probability that astolen automobile will be found within a week._________________________ 2. A company has installed a generator to back up the power incase there is a power failure. The probability of a powerfailure in a snowstorm is .30. The probabaility that the generatorwill stop working during the snowstorm is .09. What is theprobability that during the snowstorm the company will loose bothsources of power? _____________________________ 3. A tri-motor plane has three engines - a central engine andan engine on each wing. The plane will crash only if the centralengine fails and at least one of the two wing engines fail. Theprobability of failure during any given flight is .005 for thecentral engine and .008 for each of the wing engines. Assuming thatthe three engines operate independently, what is the probabilitythat the plane will crash during flight? _________ 1. In a certain city, the probability that an automobile willbe stolen and found within one week is 0.0009. The probability thatan automobile will be stolen is 0.0015. Find the probability that astolen automobile will be found within a week._________________________ 2. A company has installed a generator to back up the power incase there is a power failure. The probability of a powerfailure in a snowstorm is .30. The probabaility that the generatorwill stop working during the snowstorm is .09. What is theprobability that during the snowstorm the company will loose bothsources of power? _____________________________ 3. A tri-motor plane has three engines - a central engine andan engine on each wing. The plane will crash only if the centralengine fails and at least one of the two wing engines fail. Theprobability of failure during any given flight is .005 for thecentral engine and .008 for each of the wing engines. Assuming thatthe three engines operate independently, what is the probabilitythat the plane will crash during flight? _________Explanation / Answer
1. let S= automobile stolen in a weekF= automobile found in a week probability that an automobile will be stolen and found withina week=P(S and F) = 0.0009 probability that an automobile will be stolen=P(S)=0.0015 probability that a stolen automobile will be found within aweek, P(F/S)=P(S and F) / P(S) =0.0009 / 0.0015 =0.6 2.probability of power failure during storm, P(S) =0.30 probability of generator failure during snowstorm, P(G)=0.09 probability that during a snowstorm company will lose both thesources of power, P(S and G) =0.3 x 0.09=0.027 3. the plane will crash in the following two case: (i) central engine fails and only one of the wing enginefails. here probability = 2 x 0.005 x 0.008 x (1-0.008) =0.00007936 (ii) central engine fails and both the wing enginefails. here probability = 0.005 x 0.008 x 0.008 =0.00000032 hence total probability that the plane will crash=0.00007936 +0.00000032 = 0.00007968
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