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.
texted while driving
drove when drinking alcohol?
yes
no
yes
693
2860
no
135
4464
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 total number of drivers

Total number of drivers \(=693 + 135+2860 + 4464=8152\)

Step2: Calculate probability for the first - selected driver

Probability that the first - selected driver drove when drinking alcohol \(P_1=\frac{693 + 135}{8152}=\frac{828}{8152}\)

Step3: Calculate probability for the second - selected driver

After the first selection (without replacement), the number of remaining drivers is \(n = 8152-1 = 8151\), and the number of drivers who drove when drinking alcohol is \(m=828 - 1=827\). So \(P_2=\frac{827}{8151}\)

Step4: Calculate probability for the third - selected driver

After the second selection (without replacement), the number of remaining drivers is \(n = 8151-1 = 8150\), and the number of drivers who drove when drinking alcohol is \(m = 827-1=826\). So \(P_3=\frac{826}{8150}\)

Step5: Calculate probability for the fourth - selected driver

After the third selection (without replacement), the number of remaining drivers is \(n = 8150-1 = 8149\), and the number of drivers who drove when drinking alcohol is \(m = 826-1=825\). So \(P_4=\frac{825}{8149}\)

Step6: Calculate the combined probability

Using the multiplication rule for dependent events \(P = P_1\times P_2\times P_3\times P_4\)

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Answer:

\(0.000010\)