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 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: Identify relevant values

We want $P(\text{wore seat - belt}|\text{did not survive})$. The number of non - surviving drivers who wore seat - belts is 540, and the total number of non - surviving drivers is 2228.

Step2: Apply conditional probability formula

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, $P(\text{wore seat - belt}|\text{did not survive})=\frac{\text{Number of non - surviving drivers who wore seat - belts}}{\text{Total number of non - surviving drivers}}=\frac{540}{2228}$.

Step3: Calculate decimal and fraction

As a fraction: $\frac{540}{2228}=\frac{135}{557}$.
As a decimal: $\frac{540}{2228}\approx0.242$.

Answer:

The probability as a decimal is $0.242$.
The probability as a fraction is $\frac{135}{557}$.