A television game has 6 shows doors, of which the contests must pick 2. behind two of the doors are expensive cars, and behind the other 4 doors are consolation prizes. Find the probability that the contestant wins exactly 1 car? no car? or atleast one car?

For there to be 1 car, we consider two possible outcomes:

The first door opened has a car or the second door opened has a car.

P (1 car) = 2/6 x 4/5 + 4/6 x 2/5

P (1 car) = 8/15

For there to be no car in either door

P (no car) = 4/6 x 3/5

P (no car) = 2/5

Probability of at least one car is the sum of the probability of one car and probability of two cars:

P (2 cars) = 2/6 x 1/5

= 1/15

P (1 car) + P (2 cars) = 8/15 + 1/15

= 3/5