Answer to Question #81057 in Statistics and Probability for Liza

Question

Liza lives in a small town. In her town, it’s rainy one third of the days. Given that it is rainy, there will be heavy traffic with probability 0.5 and given that it is not rainy, there will be heavy traffic with probability 0.25. If it’s rainy and there is heavy traffic, Liza arrive late for work with probability 0.5. On the other hand, the probability of being late is reduced to 0.125 if it is not rainy and there is no heavy traffic. In other situation (rainy and no traffic, not rainy and traffic) the probability of being late is 0.25. Assume Liza pick a random day.

i. What is the probability that it’s not raining and there is heavy traffic and Liza is not late for work?
ii. What is the probability that Liza is late for work?
iii. Given that Liza arrived late at work, what is the probability that it rained that day?