Question

When a man observed a sobriety checkpoint conducted by a police​ department, he saw 695 drivers were screened and 5 were arrested for driving while intoxicated. Based on those​ results, we can estimate that Upper P (Upper W )equals0.00719​, where W denotes the event of screening a driver and getting someone who is intoxicated. What does Upper P (Upper W overbar )​denote, and what is its​ value?

Answer 1

`P(\overline{W})=0.99281`

Explanation:

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

Out of 695 drivers, the man observed that 5 were arrested for driving while intoxicated.

Therefore:
`P(W)=(5)/(695) \approx 0.00719`

The probability of the complement of event W,
`\overline{W}` denotes the probability of screening a driver and getting someone who is NOT intoxicated.

From probability theory, we know that the sum of the probability of an event and its complement is 1.

`P(W)+P(\overline{W})=1\\P(\overline{W})=1-P(W)\\=1-0.00719\\\\P(\overline{W})=0.99281`