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.

	wore seat belt	no seat belt	total
driver died	458	2169	2627
total	410,761	163,423	574,184

find the probability of wearing a seat belt, given that the driver did not survive a car accident.

the probability as a decimal is \\(\square\\).
(round to three decimal places as needed.)

the probability as a fraction is \\(\square\\).
(type an integer or a fraction.)

Explanation:

Step1: Identify conditional probability components

We need \( P(\text{seat belt} | \text{driver died}) = \frac{\text{seat belt and died}}{\text{total died}} \)

Step2: Get values from table

Seat belt and died = 458; total died = 2627

Step3: Calculate decimal probability

\( \frac{458}{2627} \approx 0.174 \)

Step4: Write as fraction

Simplify \( \frac{458}{2627} \) (no common factors)

Answer:

The probability as a decimal is 0.174
The probability as a fraction is \( \frac{458}{2627} \)