SOLUTION: Sam is fond of taking long-distance trips. During each trip his car has a tire failure in each 100-mile stretch with a probability of 0.05. He recently embarked on an 800-mile trip

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Question 1113823: Sam is fond of taking long-distance trips. During each trip his car has a tire failure in each 100-mile stretch with a probability of 0.05. He recently embarked on an 800-mile trip and took two spare tires with him on the trip.
a. What is the probability that the first change of tire occurred 300 miles from his starting point?
b. What is the probability that his second change of tire occurred 500 miles from his starting point?
c. What is the probability that he completed the trip without having to change tires?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Sam is fond of taking long-distance trips. During each trip his car has a tire failure in each 100-mile stretch with a probability of 0.05. He recently embarked on an 800-mile trip and took two spare tires with him on the trip.
a. What is the probability that the first change of tire occurred 300 miles from his starting point?
Event description:: (no)(no)(yes) = 0.95^2*0.05 = 0.0451
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b. What is the probability that his second change of tire occurred 500 miles from his starting point?
Event description: (one in the 1st 400 miles)*(0.05)
= 4C1*0.05*0.95^4 * 0.05
= 4*0.05*0.8145*0.05
= 0.008145
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c. What is the probability that he completed the trip without having to change tires?
0.95^8 = 0.6634
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Cheers,
Stan H.
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