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# Fault Tree Problem: Calculating probabilities.

Assume the probability of a tire blowout is 0.178% per 50,000 miles of use and that a person travels 15,000 miles per year in a car. Assume that the probability of loss of control is 60% if the blowout occurs on the front tires and 20% for the rear tires. If control is lost, the probability is 50% of veering to the right and 50% of veering to the left. If it goes left, the car spends 1 sec crossing the one lane of oncoming traffic (2000 vehicles/hour). Either way it goes, it ends up on the roadside, with a 20% chance of hitting a barrier or tree, if not hit by oncoming traffic. Assume there is a 20% chance of death if the car hits a barrier or tree and a 50% chance of death if hit by oncoming traffic. Calculate the probability of being killed per year in this type of accident

Hint: This is a fault tree problem. Practice with a simpler example from the readings/notes. When working the real problem, sum up all the ways of having a fatal accident and their probabilities.

#### Solution Preview

I've been working for weeks on this and have not been able to solve, please help me.
Assume the probability of a tire blowout is 0.178% per 50,000 miles of use and that a person travels 15,000 miles per year in a car. Assume that the probability of loss of control is 60% if the blowout occurs on the front tires and 20% for the rear tires. If control is lost, the probability is 50% of veering to the right and 50% of veering to the left. If it goes left, the car spends 1 sec crossing the one lane of oncoming traffic (2000 vehicles/hour). Either way it goes, it ends up on the roadside, with a 20% chance of hitting a barrier or tree, if not hit by oncoming traffic. Assume there is ...

#### Solution Summary

Fault tree problems are analyzed to calculate the probabilities.

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