Question

A study of teenage drivers found that 53% text while driving and 26% have a car accident in their first year of driving. 11% of teenage drivers text while driving AND have a car accident in their first year. Find the probability that a teenager gets into an accident in the first year of driving, given that he or she texts while driving. Round your answer to the nearest hundredth. Group of answer choices

0. 14

0. 21

0. 42

0. 49

Answer 1

To find the probability that a teenager gets into an accident in the first year of driving, given that he or she texts while driving, we can use conditional probability.

Let's denote the event of texting while driving as T and the event of having a car accident in the first year of driving as A. We are given the following probabilities:

P(T) = 53% = 0.53 (probability of texting while driving)
P(A) = 26% = 0.26 (probability of having a car accident in the first year)
P(T and A) = 11% = 0.11 (probability of texting while driving and having a car accident)

We can use the formula for conditional probability:
P(A|T) = P(T and A) / P(T)

Substituting the given values:
P(A|T) = 0.11 / 0.53 ≈ 0.2075

Rounding the answer to the nearest hundredth, the probability that a teenager gets into an accident in the first year of driving, given that he or she texts while driving, is approximately 0.21.

Therefore, the answer closest to the given choices is 0.21.