A toll bridge charges $2 for passenger cars and $4.5 for other vehicles. Suppose that 80% of all cars passing from this bridge are passenger cars. If in a day40 vehicles cross the bridge, compute the expected toll revenue from all thesevehicles. You should use terminology of random variables to justify your steps. Hint: Let X be the number of passenger cars, then the toll revenue is a linearfunction of X ...

Let a be the total passenger cars

Let b be the total other vehicles

Let r be the toll revenue

Given that passenger rate is $2 and other vehicles rate is $4.5, the toll revenue can be calculated using the linear function as follows:

r = 2a + 4.5b

Given that 80% of all cars are passenger cars and the total vehicles is 40

a = 0.8 x 40 = 32

b = 0.2 x 40 = 8

r = 2a + 4.5b = (2 x 32) + (4.5 x 8) = 64 + 36 = 100

The expected toll revenue is $100