Questions: 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? Yes No Texted While Driving 682 2926 No Texting While Driving 141 4342 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.) 1.

Solution Steps

The total number of drivers who drove when drinking alcohol is the sum of those who texted while driving and those who did not: \[ \text{Total drivers who drove when drinking alcohol} = 682 + 141 = 823 \]

The total number of drivers surveyed is the sum of all drivers who texted while driving and those who did not: \[ \text{Total drivers} = (682 + 2926) + (141 + 4342) = 8091 \]

The probability \( p \) that a randomly selected driver drove when drinking alcohol is given by: \[ p = \frac{\text{Total drivers who drove when drinking alcohol}}{\text{Total drivers}} = \frac{823}{8091} \approx 0.1017 \]

The probability that four different high school drivers all drove when drinking alcohol is: \[ P(\text{All four drove when drinking alcohol}) = p^4 = (0.1017)^4 \approx 0.000107 \]

Final Answer