Question

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.

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.)

Explanation:

Step1: Calculate the total number of high - school drivers

The total number of high - school drivers is \(700 + 3271+169 + 4516=(700 + 169)+(3271 + 4516)=869+7787 = 8656\).

Step2: Calculate the number of drivers who drove when drinking alcohol

The number of drivers who drove when drinking alcohol is \(700+169 = 869\).

Step3: Use the multiplication rule for independent events (approximate since sampling without replacement, but with large \(n\))

The probability that the first driver drove when drinking alcohol is \(P_1=\frac{869}{8656}\).
The probability that the second driver drove when drinking alcohol (assuming independence, for large \(n\) the change is small) is \(P_2=\frac{869}{8656}\).
The probability that the third driver drove when drinking alcohol is \(P_3=\frac{869}{8656}\).
The probability that the fourth driver drove when drinking alcohol is \(P_4=\frac{869}{8656}\).

The probability that all four drove when drinking alcohol is \(P = (\frac{869}{8656})^4\).

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Answer:

\(0.000102\)