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3 years ago

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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 i

n 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%

1 answer:

nikdorinn [45]3 years ago

4 0

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

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