Questions: When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 9 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)=0.01372, 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 driver being intoxicated. B. P(W̅) denotes the probability of a driver passing through the sobriety checkpoint. C. P(W̅) denotes the probability of screening a driver and finding that he or she is not intoxicated. D. P(W̅) denotes the probability of screening a driver and finding that he or she is intoxicated. P(W̅)= (Round to five decimal places as needed.)

When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 9 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)=0.01372, 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 driver being intoxicated. B. P(W̅) denotes the probability of a driver passing through the sobriety checkpoint. C. P(W̅) denotes the probability of screening a driver and finding that he or she is not intoxicated. D. P(W̅) denotes the probability of screening a driver and finding that he or she is intoxicated. P(W̅)= (Round to five decimal places as needed.)
Transcript text: 4.22024 Question 5, 4.2.8 HW Score: 70.59\%, 12 of 17 Part 2 of 2 points Points: 0 of 1 Save When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 9 were arrested for driving while intoxicated. Based on those results, we can estimate that $P(W)=0.01372$, 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. $P(\bar{W})$ denotes the probability of driver being intoxicated. B. $\mathrm{P}(\overline{\mathrm{W}})$ denotes the probability of a driver passing through the sobriety checkpoint. C. $\mathrm{P}(\overline{\mathrm{W}})$ denotes the probability of screening a driver and finding that he or she is not intoxicated. D. $P(\bar{W})$ denotes the probability of screening a driver and finding that he or she is intoxicated. \[ P(\bar{W})= \] $\square$ (Rourh to five decimal places as needed.) View an example Get more help Clear all Check answer
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Solution

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Solution Steps

To find \( P(\overline{W}) \), we need to calculate the probability of the complement of event \( W \). Since \( P(W) \) is the probability of screening a driver and finding that they are intoxicated, \( P(\overline{W}) \) represents the probability of screening a driver and finding that they are not intoxicated. The complement rule states that \( P(\overline{W}) = 1 - P(W) \).

Step 1: Identify the Probability of Event \( W \)

We are given that the probability of screening a driver and finding that they are intoxicated is \( P(W) = 0.01372 \).

Step 2: Calculate the Complement Probability

To find the probability of the complement of event \( W \), which is denoted as \( P(\overline{W}) \), we use the complement rule: \[ P(\overline{W}) = 1 - P(W) \] Substituting the value of \( P(W) \): \[ P(\overline{W}) = 1 - 0.01372 = 0.98628 \]

Step 3: Round the Result

The value of \( P(\overline{W}) \) is already in a suitable format, so we retain it as \( 0.98628 \).

Final Answer

The probability \( P(\overline{W}) \) denotes the probability of screening a driver and finding that they are not intoxicated, and its value is \[ \boxed{P(\overline{W}) = 0.98628} \]

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