Question

the table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt. find the probability of not wearing a seat belt, given that the driver did not survive a car accident. the probability as a decimal is (round to three decimal places as needed.) the probability as a fraction is (type an integer or a fraction.)

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of this problem, let $A$ be the event of not wearing a seat - belt and $B$ be the event of not surviving. Then $P(A|B)=\frac{\text{Number of non - seat - belt and non - surviving drivers}}{\text{Number of non - surviving drivers}}$.

Step2: Identify relevant values from the table

The number of non - surviving drivers is 2538 (total number of driver deaths). The number of non - surviving drivers who did not wear a seat - belt is 2019.

Step3: Calculate the probability as a decimal

$P(A|B)=\frac{2019}{2538}\approx0.795$

Step4: Calculate the probability as a fraction

The probability as a fraction is $\frac{2019}{2538}$.

Answer:

The probability as a decimal is 0.795
The probability as a fraction is $\frac{2019}{2538}$