Question

when a man observed a sobriety checkpoint conducted by a police department, he saw 695 drivers were screened and 7 were arrested for driving while intoxicated. based on those results, we can estimate that ( p(w) = 0.01007 ), 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? (\bigcirc) a. ( p(overline{w}) ) denotes the probability of a driver passing through the sobriety checkpoint (\bigcirc) b. ( p(overline{w}) ) denotes the probability of screening a driver and finding that he or she is not intoxicated (\bigcirc) c. ( p(overline{w}) ) denotes the probability of screening a driver and finding that he or she is intoxicated (\bigcirc) d. ( p(overline{w}) ) denotes the probability of driver being intoxicated. ( p(overline{w}) = square ) (round to five decimal places as needed.)

Explanation:

Step1: Understand Complementary Probability

The event \(\overline{W}\) is the complement of event \(W\). For any event \(W\), the probability of its complement \(P(\overline{W})\) satisfies \(P(W)+P(\overline{W}) = 1\). Here, \(W\) is the event of screening a driver and finding them intoxicated, so \(\overline{W}\) is screening a driver and finding them not intoxicated.

Step2: Calculate \(P(\overline{W})\)

We know \(P(W)=0.01007\). Using the formula \(P(\overline{W})=1 - P(W)\), we substitute the value of \(P(W)\):
\(P(\overline{W})=1 - 0.01007\)
\(P(\overline{W}) = 0.98993\)

Answer:

For the first part, the correct option is B. \(P(\overline{W})\) denotes the probability of screening a driver and finding that he or she is not intoxicated. For the second part, \(P(\overline{W})=\boxed{0.98993}\)