Answer:
[tex]P(\overline{W})=0.99281[/tex]
Step-by-step 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: [tex]P(W)=\dfrac{5}{695} \approx 0.00719[/tex]
The probability of the complement of event W, [tex]\overline{W}[/tex] 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.
[tex]P(W)+P(\overline{W})=1\\P(\overline{W})=1-P(W)\\=1-0.00719\\\\P(\overline{W})=0.99281[/tex]
