Question

There is a 70% 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 90%. 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)

66%

63%

78%

29%

Answer 1

Answer:

63%

Step-by-step explanation:

This is a problem of conditional probability.

The two events that are given are:

• Car stuck in the snow - Let it be event S. P(S) = 70% = 0.70
• Require a tow truck - Let it be event T.

We have to find the probability of being stuck in the snow AND requiring a tow truck which can be given as P(S and T)

We are also given the conditional probability, which is P(T | S) = 90% = 0.90

Using the given formula for our case we can modify the formula as:

$P(T|S)=\frac{P(S \cap T)}{P(S)}$

$0.90=\frac{P(S \cap T)}{0.70}\\\\ P(S \cap T)=0.90 \times 0.70\\\\ P(S \cap T)=0.63$

Therefore, there is 63% (0.63) chance that you will get stuck in the snow with your car AND require a tow truck to pull you out