The table summarizes results from pedestrian deaths that were caused by automobile accidents. Pedestrian Deaths Driver Intoxicated? Pedestrian Intoxicated? Yes No Yes 50 73 No 245 614 If two different pedestrian deaths are randomly selected, find the probability that they both involved drivers that were not intoxicated. Report the answer rounded to four decimal place accuracy.

To solve this problem, we need to calculate the probability that both selected pedestrian deaths involved drivers that were not intoxicated.

### Step 1: Calculate the total number of pedestrian deaths
We sum up all the values in the table to find the total number of pedestrian deaths.

\[
\text{Total} = 50 + 73 + 245 + 614 = 982
\]

### Step 2: Determine the number of pedestrian deaths where the driver was not intoxicated
We sum the values where the driver was not intoxicated:

\[
\text{Driver Not Intoxicated} = 73 + 614 = 687
\]

### Step 3: Calculate the probability that the first death involved a driver that was not intoxicated
\[
P(\text{First death, driver not intoxicated}) = \frac{687}{982}
\]

### Step 4: Calculate the probability that the second death involved a driver that was not intoxicated, given the first one was
If the first death already involved a driver that was not intoxicated, the remaining number of such cases would be \(687 - 1 = 686\) and the total number of remaining cases would be \(982 - 1 = 981\).

\[
P(\text{Second death, driver not intoxicated | First death, driver not intoxicated}) = \frac{686}{981}
\]

### Step 5: Calculate the combined probability for both events
The probability that both pedestrian deaths involved drivers that were not intoxicated is the product of the two individual probabilities:

\[
P(\text{Both deaths, drivers not intoxicated}) = \frac{687}{982} \times \frac{686}{981}
\]

Now, let's calculate this:

\[
P = \frac{687 \times 686}{982 \times 981} \approx \frac{471282}{963942} \approx 0.4889
\]

So, the probability that both selected pedestrian deaths involved drivers that were not intoxicated is approximately **0.4889** when rounded to four decimal places.

Do you want more details or have any questions? 

Here are 5 related questions to further explore the topic:
1. What is the probability that both selected deaths involved intoxicated drivers?
2. How would the probability change if only one death was randomly selected?
3. What is the probability that at least one of the selected deaths involved a driver that was intoxicated?
4. If the driver was not intoxicated, what is the probability that the pedestrian was intoxicated?
5. How does the probability of both drivers being intoxicated compare to both not being intoxicated?

**Tip:** Always check whether the events are dependent or independent before calculating combined probabilities.

This guide explains how to calculate the probability that two randomly selected pedestrian deaths involved drivers that were not intoxicated. Learn step-by-step how to apply the rules of probability, including conditional probability and the multiplication rule. Suitable for Grades 10-12.

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