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. (show work)

Solution

Answer : 0.925

For getting the probability to reach class on time in cold weather , we need to consider both the scenarios (i.e taking a bus and drive car)

(i) Drive car:

In this case , probability of getting to class on time = 0.9 * 0.95 = 0.855

(ii) Taking bus:

In this case , probability of getting to class on time = 0.1 * 0.7 = 0.07

So,

The probability you get to class on time in cold weather = 0.855 + 0.07 = 0.925 Answer