The table summarizes results from pedestrian deaths that were caused by automobile accidents. Pedestrian Deaths Driver Intoxicated? Pedestrian Intoxicated? Yes No Yes 57 85 No 269 577 If two different pedestrian deaths are randomly selected, find the probability that they both involved pedestrians that were intoxicated. Report the answer rounded to four decimal place accuracy.

To find the probability that both selected pedestrian deaths involved intoxicated pedestrians, we'll follow these steps:

1. **Calculate the Total Number of Pedestrian Deaths:**
   Add up all the values in the table to find the total number of pedestrian deaths.

   \[
   \text{Total} = 57 + 85 + 269 + 577 = 988
   \]

2. **Calculate the Total Number of Pedestrian Deaths Where Pedestrians Were Intoxicated:**
   Add the numbers in the rows where the pedestrian was intoxicated.

   \[
   \text{Total Intoxicated Pedestrians} = 57 + 85 = 142
   \]

3. **Calculate the Probability of Selecting Two Intoxicated Pedestrians:**
   The probability of selecting one intoxicated pedestrian is the ratio of intoxicated pedestrians to the total number of pedestrian deaths. After selecting the first intoxicated pedestrian, the probability of selecting a second one from the remaining pedestrians is the ratio of the remaining intoxicated pedestrians to the remaining total number of pedestrians.

   \[
   P(\text{Both Intoxicated}) = \frac{142}{988} \times \frac{141}{987}
   \]

4. **Calculate the Exact Probability:**
   
   \[
   P(\text{Both Intoxicated}) = \frac{142 \times 141}{988 \times 987}
   \]

   \[
   P(\text{Both Intoxicated}) \approx \frac{20022}{975156} \approx 0.02054
   \]

5. **Final Answer:**
   The probability that both selected pedestrian deaths involved intoxicated pedestrians is approximately **0.0205** when rounded to four decimal places.

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Do you want more details or have any questions? 

Here are 5 related questions to consider:
1. What is the probability of selecting two non-intoxicated pedestrians?
2. How would the probability change if the number of pedestrian deaths increased?
3. What is the probability of selecting one intoxicated and one non-intoxicated pedestrian?
4. How can we apply these probabilities to predict future pedestrian deaths?
5. What is the significance of considering driver intoxication in this context?

**Tip:** Always double-check your calculations by breaking down each step to ensure accuracy, especially in probability problems involving multiple selections.

Find the probability of selecting two intoxicated pedestrians from a dataset of pedestrian deaths caused by automobile accidents. This detailed solution covers essential probability concepts and includes a step-by-step calculation, making it suitable for Grades 10-12.

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