Problem

Use the data in the following table, which lists survey results from high school drivers at least 16 years of age. Assume that subjects are randomly selected from those included in the table.
Drove When Drinking Alcohol?
\begin{tabular}{|l|c|c|}
\hline & Yes & No \\
\hline Texted While Driving & 693 & 3068 \\
\hline No Texting While Driving & 122 & 4210 \\
\hline
\end{tabular}
If four different high school drivers are randomly selected, find the probability that they all drove when drinking alcohol.
The probability that four randomly selected high school drivers all drove when drinking alcohol is (Round to six decimal places as needed.)

Answer

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Answer

Final Answer: The probability that four randomly selected high school drivers all drove when drinking alcohol is approximately \(\boxed{0.000103}\).

Steps

Step 1 :First, calculate the total number of high school drivers surveyed by adding all the numbers in the table. The total number of drivers is \(693 + 3068 + 122 + 4210 = 8093\).

Step 2 :Next, find the number of drivers who drove when drinking alcohol. This is the sum of the 'Yes' column, which is \(693 + 122 = 815\).

Step 3 :Calculate the probability of a single driver having driven when drinking alcohol. This is the number of drivers who drove when drinking alcohol divided by the total number of drivers. The probability is \(\frac{815}{8093} \approx 0.1007043123687137\).

Step 4 :Since we are selecting four drivers, and we are assuming that the selection of each driver is independent, the probability that all four drove when drinking alcohol is the product of the individual probabilities. Therefore, the probability is \((0.1007043123687137)^4 \approx 0.00010284715282701562\).

Step 5 :Final Answer: The probability that four randomly selected high school drivers all drove when drinking alcohol is approximately \(\boxed{0.000103}\).

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