Question

A television game show has 12 ​doors, of which the contestant must pick 2.

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

2 doors she selects. Determine the probability that the contestant wins at least one car.

Answer 1

Answer:

Given,

To determine the probability that the contestant wins at least one car

consider,

Total number of combinations = 12C2

= (12*11)/2*1

= 66

P(Exactly one car) = 3C1*9C1

= 3*9

= 27

P(Exactly two car) = 3C2

= 3

Required probability = [P(Exactly one car) + P(Exactly two cars)] / Total combinations

= [27 + 3]/66

= 30/66

= 0.4545