There are two locations in town (north and south) under consideration for a new restaurant, but only one location will actually become available. If it is built in the north, the restaurant stands a 90% chance of successfully surviving its first year. However, if it is built in the south, its chances of survival are only 65%. It is estimated that the chances of the northern location being available are 40%.
a. Draw a probability tree for this situation, with the first branch being "location."
b. Find the probability that the restaurant will survive its first year.
c. Find the probability that the restaurant is built in the south and is successful.
d. Find the probability that the restaurant is in the south given that it is successful.
e. Find the probability of failure given that it is in the north.