use the data in the following table, which lists survey results from high - school drivers at least 16 years…

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.\n\n| |drove when drinking alcohol?| |\n|--|--|--|\n| |yes|no|\n|texted while driving|736|3121|\n|no texting while driving|166|4210|\n\nif four different high - school drivers are randomly selected, find the probability that they all drove when drinking alcohol.\n\nthe probability that four randomly selected high - school drivers all drove when drinking alcohol is \n(round to six decimal places as needed.)

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.\n\n| |drove when drinking alcohol?| |\n|--|--|--|\n| |yes|no|\n|texted while driving|736|3121|\n|no texting while driving|166|4210|\n\nif four different high - school drivers are randomly selected, find the probability that they all drove when drinking alcohol.\n\nthe probability that four randomly selected high - school drivers all drove when drinking alcohol is \n(round to six decimal places as needed.)

Answer

Explanation:

Step1: Calculate total number of drivers

First, find the total number of high - school drivers by adding all the values in the table. $736 + 3121+166 + 4210=8233$

Step2: Calculate probability of one driver driving when drinking

The number of drivers who drove when drinking is $736 + 166=902$. The probability $p$ that a single randomly selected driver drove when drinking is $\frac{902}{8233}$.

Step3: Calculate probability of four drivers all driving when drinking

Since the selections are independent, the probability that four different randomly selected drivers all drove when drinking is $p^4$. $p^4=\left(\frac{902}{8233}\right)^4=\left(0.10956\right)^4\approx0.000142$

Answer:

$0.000142$