Probability

Question

2a. Samantha goes to school five days a week. when it rains, the probability that she goes to school by bus is 0.5. When it does not rain, the probability that she goes to school by bus is 0.3. The probability that it rains on any given day is .2

On a randomly selected school day, find the probability that Samantha goes to school by bus.

2b. Find the probability that it was raining, given that samantha went to school by bus

Answer 1

 Weather     Transport      Overall Probability

 Rain 0.2     Bus 0.5               0.10

                  Walk 0.5             0.10

Fair 0.8       Bus 0.3               0,24

                  Walk 0.7             0.56

 

a) P(bus used) = 0.10 + 0.24 = 0.34

 

b) P(rain|bus was used) = 0.10 / 0.10+0.0.24 = 0.294 (actually exactly 5/17)