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Chapter 4: Q8 (page 156)

Sobriety Checkpoint When the author observed a sobriety checkpoint conducted by the Dutchess County Sheriff Department, he saw that 676 drivers were screened and 6 were arrested for driving while intoxicated. Based on those results, we can estimate that PI= 0.00888, where I denotes the event of screening a driver and getting someone who is intoxicated. What doesPI¯ denote, and what is its value?

Short Answer

Expert verified

PI¯represents screening a driver who is not intoxicated. Its value is equal to 0.99112.

Step by step solution

01

Given information

The probability of screening a driver who is intoxicated is denoted by PIand is equal to 0.00888.

02

Define complementary events

Let E be an event. Then, represents the event “not E.”

E¯is called thecomplementof E and vice-versa.

The below property is followed by two complementary events:

PE+PE¯=1

03

Define and compute the probability of a complementary event

Let I be the event of screening a driver who is intoxicated.

Therefore, I¯is the event of all outcomes that are not included in event I.

Thus, the probability of the complement of the event I is expressed as follows:

PI¯=1-PI=1-0.00888=0.991

Thus,PN¯ is equal to 0.991.

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