Questions: When a man observed a sobriety checkpoint conducted by a police department, he saw 667 drivers were screened and 4 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)=0.00600, where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W̅) denote, and what is its value? What does P(W̅) represent? A. P(W̅) denotes the probability of a driver passing through the sobriety checkpoint. B. P(W̅) denotes the probability of screening a driver and finding that he or she is intoxicated. C. P(W̅) denotes the probability of driver being intoxicated. D. P(W̅) denotes the probability of screening a driver and finding that he or she is not intoxicated. P(W̅)= (Round to five decimal places as needed.)

When a man observed a sobriety checkpoint conducted by a police department, he saw 667 drivers were screened and 4 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)=0.00600, where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W̅) denote, and what is its value?

What does P(W̅) represent?
A. P(W̅) denotes the probability of a driver passing through the sobriety checkpoint.
B. P(W̅) denotes the probability of screening a driver and finding that he or she is intoxicated.
C. P(W̅) denotes the probability of driver being intoxicated.
D. P(W̅) denotes the probability of screening a driver and finding that he or she is not intoxicated.
P(W̅)=
(Round to five decimal places as needed.)

Transcript text: When a man observed a sobriety checkpoint conducted by a police department, he saw 667 drivers were screened and 4 were arrested for driving while intoxicated. Based on those results, we can estimate that $\mathrm{P}(\mathrm{W})=0.00600$, where W denotes the event of screening a driver and getting someone who is intoxicated. What does $\mathrm{P}(\overline{\mathrm{W}})$ denote, and what is its value? What does $\mathrm{P}(\overline{\mathrm{W}})$ represent? A. $\mathrm{P}(\overline{\mathrm{W}})$ denotes the probability of a driver passing through the sobriety checkpoint. B. $P(\bar{W})$ denotes the probability of screening a driver and finding that he or she is intoxicated. C. $P(\bar{W})$ denotes the probability of driver being intoxicated. D. $P(\bar{W})$ denotes the probability of screening a driver and finding that he or she is not intoxicated. $P(\bar{w})=$ $\square$ (Round to five decimal places as needed.)

Solution

Solution Steps

To solve this problem, we need to understand the concept of complementary probability. The probability of the complement of an event $ \overline{W} $ is calculated as $ 1 - P(W) $. Here, $ P(W) $ is given as 0.00600. We need to find $ P(\overline{W}) $ and understand what it represents.

Solution Approach

Identify the given probability $ P(W) $.
Calculate the complementary probability $ P(\overline{W}) $ using the formula $ P(\overline{W}) = 1 - P(W) $.
Determine the correct interpretation of $ P(\overline{W}) $ from the given options.

Step 1: Identify the Given Probability

We are given the probability of screening a driver and finding that he or she is intoxicated, denoted as $ P(W) $. The value of $ P(W) $ is 0.00600.

Step 2: Calculate the Complementary Probability

The complementary probability $ P(\overline{W}) $ represents the probability of screening a driver and finding that he or she is not intoxicated. This can be calculated using the formula: \[ P(\overline{W}) = 1 - P(W) \]

Substituting the given value: \[ P(\overline{W}) = 1 - 0.00600 = 0.99400 \]

Step 3: Interpret the Complementary Probability

From the given options, $ P(\overline{W}) $ denotes the probability of screening a driver and finding that he or she is not intoxicated. This corresponds to option D.

Final Answer

$\boxed{0.99400}$

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