Q8 Sobriety Checkpoint When the aut... [FREE SOLUTION]

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 $P (I)$ = 0.00888, where I denotes the event of screening a driver and getting someone who is intoxicated. What does $P (\overset{炉}{I})$ denote, and what is its value?

Expert verified

$P (\overset{炉}{I})$ represents screening a driver who is not intoxicated. Its value is equal to 0.99112.

The probability of screening a driver who is intoxicated is denoted by $P (I)$ and is equal to 0.00888.

Let E be an event. Then, represents the event 鈥渘ot E.鈥�

$\overset{炉}{E}$ is called thecomplementof E and vice-versa.

The below property is followed by two complementary events:

$P (E) + P (\overset{炉}{E}) = 1$

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

Therefore, $\overset{炉}{I}$ 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:

$P (\overset{炉}{I}) = 1 - P (I) = 1 - 0.00888 = 0.991$

Thus, $P (\overset{炉}{N})$ is equal to 0.991.

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