Janice has noticed that on her drive to work, there are several things that can slow her down. First, she hits a red light with probability .3. If she hits the red light, she also has to stop for the commuter train with probability .4, but if she doesn't hit the red light, she has to stop with only probability .2.
a. Find the probability that Janice has to stop for both the red light and the train.
b. Find the probability that Janice has to stop for the red light given that she has to stop for the commuter train.
c. Explain how you would conduct a simulation to estimate the probabilities in parts (a) and (b).
d. Conduct the simulation described in part (c). Use at least 50 repetitions.
e. Compare the answers that you computed in parts (a) and (b) to the estimated probabilities from your simulation in part (d).