Question

There is a 40% chance that your car will get stuck in the snow during the next big snow fall. Given that you are already stuck in the snow with your car, the chance that you will require a tow truck to pull you out is 75%. What is the chance that you will get stuck in the snow with your car AND require a tow truck to pull you out?

Hint: P(A|B)=P(A∩B) / P(B)


53%


30%


32%


28%

Answer 1

30%

Explanation:

We need to find the probability of getting stuck in the snow and require a tow truck to be pulled out, this is a problem of conditional probability.

When two events A and B are dependent the probability of one event ocurring given the other is:

P(A|B)=P(A∩B) / P(B) (1)

In this case A= Requiring a Tow truck and B= Getting Stuck in the snow.

From equation (1) we can conclude that, the probability of requiring a tow truck given that we are stuck in the snow equals the probability of both events ocurring divided by the probability of getting stuck in the snow.

The probability of getting a tow truck given that you are stuck is P(A|B)=0.75, while de probability of getting stuck is P(B)=0.4. Substituting this values in equation (1) , and solving for P(A∩B) we get that the probability of of getting stuck in the snow and require a tow truck to pull you out is P(A∩B)=0.4*0.75 = 0.30.