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.

drove when drinking alcohol?	yes	no
no testing while driving	115	409

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 high - school drivers

The total number of high - school drivers is the sum of all values in the table: $623 + 2403+115 + 403=3544$.

Step2: Calculate probability of one driver driving when drinking

The number of drivers who drove when drinking is $623 + 115=738$. The probability $p$ that a single randomly selected driver drove when drinking is $p=\frac{738}{3544}$.

Step3: Calculate probability of 4 drivers all driving when drinking

Since the selections are independent, the probability that 4 different randomly selected drivers all drove when drinking is $P = (\frac{738}{3544})^4$.
\[

$$\begin{align*} P&=(\frac{738}{3544})^4\\ &=(\frac{369}{1772})^4\\ &\approx(0.20824)^4\\ &\approx0.0018 \end{align*}$$

\]

Answer:

$0.0018$