Question

1. Before heading out to college, Tina always checks the CTA schedule. The recommendation is to take the train 60% of the time and to take the bus the remaining 40%. The recommended train is on time with probability 0.8. The bus is slightly less reliable, only making it on time with probability 0.7. (a) What’s the probability that Tina is on time? (b) Tina is late. What’s the probability she took the bus? Rami is not as diligent. He forgets to check the schedule a quarter of the time. When this happens, he tosses a fair coin to choose between the train and the bus. Because his choice is not the best, no matter which mode of transportation he chooses, he ends up being late 2 out of 5 times. (c) Rami says he took the train. What’s the probability he checked the schedule? (d) You then learn from Tina that Rami was in fact late. Now what’s the probability he checked the schedule?

Answer 1