1. A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 20%. She also believes that if the economy enters a recession, the probability that her mutual fund will increase in value is 20%. If there is no recession the probability that the mutual fund will increase in value is 75%. Find the probability that the mutual fund's value will increase.

2. Three airlines serve a small town in the country. Air A has 50% of all the scheduled flights, Air B has 30%, and Air C has the remaining flights. Their on-time rates are 40%, 65%, and 80%, respectively. A plane has just left on time. What is the probability that it was Air A?