Question

the table summarizes results from 987 pedestrian deaths that were caused by automobile accidents. pedestrian deaths driver intoxicated? pedestrian intoxicated? yes no yes 55 71 no 227 634 if one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was intoxicated. please enter a decimal to 4 decimal places. probability =

Explanation:

Step1: Define the formula for probability

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that the pedestrian was not intoxicated and \(B\) be the event that the driver was intoxicated.

Step2: Calculate the number of total cases

The total number of pedestrian - deaths is \(n = 987\).

Step3: Calculate \(P(A)\)

The number of cases where the pedestrian was not intoxicated is \(71 + 634=705\). So \(P(A)=\frac{705}{987}\).

Step4: Calculate \(P(B)\)

The number of cases where the driver was intoxicated is \(55 + 71 = 126\). So \(P(B)=\frac{126}{987}\).

Step5: Calculate \(P(A\cap B)\)

The number of cases where the pedestrian was not intoxicated and the driver was intoxicated is \(71\). So \(P(A\cap B)=\frac{71}{987}\).

Step6: Calculate \(P(A\cup B)\)

\[

$$\begin{align*} P(A\cup B)&=\frac{705}{987}+\frac{126}{987}-\frac{71}{987}\\ &=\frac{705 + 126-71}{987}\\ &=\frac{760}{987}\\ &\approx0.7700 \end{align*}$$

\]

Answer:

\(0.7700\)