Question

A television game show has 12 ​doors, of which the contestant must pick 3. Behind 3 of the doors are expensive​ cars, and behind the other 9 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she selects. Determine the probability that the contestant wins at least one car.

Answer 1

The probability that the contestant wins at least one car is 3/5.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

For 1 car, we consider two possible outcomes:

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

P(1 car) = 8/15

For no car in either door

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

P(no car) = 2/5

The probability that the contestant wins at least one car is the sum of the probability of one car and the 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

Learn more about probability here;

brainly.com/question/11234923

#SPJ1