Question

when a man observed a sobriety checkpoint conducted by a police department, he saw 652 drivers were screened and 4 were arrested for driving while intoxicated. based on those results, we can estimate that p(w)=0.00613, where w denotes the event of screening a driver and getting someone who is intoxicated. what does p(\overline{w}) denote, and what is its value? what does p(\overline{w}) represent? a. p(\overline{w}) denotes the probability of screening a driver and finding that he or she is not intoxicated. b. p(\overline{w}) denotes the probability of a driver passing through the sobriety checkpoint. c. p(\overline{w}) denotes the probability of driver being intoxicated. d. p(\overline{w}) denotes the probability of screening a driver and finding that he or she is intoxicated.

Explanation:

In probability, $\overline{W}$ is the complement of event $W$. Since $W$ is the event of screening a driver and getting someone who is intoxicated, $\overline{W}$ is the event of screening a driver and getting someone who is not intoxicated. The probability of an event and its complement satisfy $P(W)+P(\overline{W}) = 1$.

Answer:

A. P($\overline{W}$) denotes the probability of screening a driver and finding that he or she is not intoxicated.

First, we know that $P(W)=0.00613$.
Since $P(W)+P(\overline{W}) = 1$, we can calculate $P(\overline{W})$ as follows:
$P(\overline{W})=1 - P(W)$
$P(\overline{W})=1 - 0.00613=0.99387$