Your car has trouble starting in cold weather and only has a

Your car has trouble starting in cold weather, and only has a .9 probability of starting in the morning. If it doesn’t start, you have to take the bus. If you get to drive your car, you have a .95 probability of getting to class on time. If you take the bus, you only have a .7 probability of getting to class on time. What is the probability you get to class on time in cold weather? Hint: A tree diagram may help.

Solution

By Bayes Rule,

P(on time) = P(car) P(on time|car) + P(bus) P(on time|bus)

As

P(bus) = 1 - P(car) = 0.1,

Thus,

P(on time) = 0.9 * 0.95 + 0.1 * 0.7 = 0.925 [ANSWER]