Question

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?

Answer 1

`P(\overline W)=0.98957`

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,
`P(W)=(7)/(671)=0.01043`

• The Probability
  `P(\overline W)` 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,

`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`