A certain university has 20 vehicles available for use by faculty and staff. Eight of these are vans and 12 are cars. On a particular day, only two requests for vehicles have been made. Suppose that the two vehicles to be assigned are chosen at random from the 20 vehicles available. (a) Let E denote the event that the first vehicle assigned is a van. What is P(E)? (b) Let F denote the probability that the second vehicle assigned is a van. What is P(F| E)? (c) Use the results of parts (a) and (b) to calcula Ite P(E n F). Step 1 (a) Let E denote the event that the first vehicle assigned is a van. What is P(E)? Recall that E denotes the event that the first vehicle assigned is a van. Therefore, P(E) is the probability that the first vehicle assigned is a van. We are given that there are 20 total vehicles: 8 vans and 12 cars. Therefore, we calculate the probability using the following formula. (Enter your answer as a fraction.) number of vans P(E) = total number of vehicles 2/5 Step 2 (b) Let F denote the probability that the second vehicle assigned is a van. What is P(F | E)? Recall that E denotes the event that the first vehicle assigned is a van and F denotes the event that the second vehicle assigned is a van. Therefore, P(FIE) is the conditional probability that the second vehicle is a van, given that the first vehicle is a van. Therefore, we calculate the probability using the following formula. number of vans left if we know that one van is already assigned P(FIE) = total number of vehicles left after one vehicle is already assigned We are given that there are 20 total vehicles: 8 vans and 12 cars. Initially there were 20 vehicles available, but one vehicle has already been assigned. Therefore, the total number of vehicles left after one vehicle is already assigned is 20 -1 = 19 Since there were initially 8 vans and we know that the first vehicle assigned was a van, that means that there are now 12 |x vans left after the first vehicle is assigned. Use these values to calculate the desired probability. (Enter your answer as a fraction.) number of vans left if we know that one van is already assigned total number of vehicles left after one vehicle is already assigned P(FIE) =