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When a man observed a sobriety checkpoint conducted by a police​ department, he saw 671671 drivers were screened and 77 were arrested for driving while intoxicated. Based on those​ results, we can estimate that Upper P (Upper W )P(W)equals=0.010430.01043​, where W denotes the event of screening a driver and getting someone who is intoxicated. What does Upper P (Upper W overbar )PW ​denote, and what is its​ value? What does Upper P (Upper W overbar )PW ​represent?

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Answer:

[tex]P(\overline W)=0.98957[/tex]

Step-by-step explanation:

Number of drivers Screened = 671

Number Arrested for Driving While Intoxicating = 7

If the W denotes the event of screening a driver and getting someone who is intoxicated.

The Probability of W, [tex]P(W)=\frac{7}{671}=0.01043[/tex]

  • The Probability [tex]P(\overline W)[/tex] is the probability of the event of screening a driver and getting someone who is not intoxicated. Simply put, it is the Probability of the Complement of W.

From Probability Theorem,

[tex]P(W)+P(\overline W)=1\\Since \: P(W)=0.01043\\0.01043+P(\overline W)=1\\P(\overline W)=1-0.01043\\=0.98957[/tex]

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