Automobile Theft Accordingto the Insurance Information Institute, in 2016 there was a 13.3 % probability that an automobile theft in the United States would be cleared by arrests. If an automobile theft case from 2016 is randomly selected, what is the probability that it was not cleared by an arrest?
Automobile Theft Accordingto the Insurance Information Institute, in 2016 there was a 13.3 % probability that an automobile theft in the United States would be cleared by arrests. If an automobile theft case from 2016 is randomly selected, what is the probability that it was not cleared by an arrest?
Solution Summary: The author calculates the probability that an automobile theft case from 2016 was not cleared by an arrest.
Automobile Theft Accordingto the Insurance Information Institute, in 2016 there was a
13.3
%
probability that an automobile theft in the United States would be cleared by arrests. If an automobile theft case from 2016 is randomly selected, what is the probability that it was not cleared by an arrest?
Expert Solution & Answer
To determine
To calculate: The probability that an automobile theft case from 2016 was not cleared by an arrest when there was a 13.3% probability that an automobile theft in the United States would be cleared by arrests.
Answer to Problem 51AYU
Solution:
The probability that an automobile theft case from 2016 was not cleared by an arrest is 0.867.
Explanation of Solution
Given information:
According to the Insurance Information institute, in 2016 there was a 13.3% probability that an automobile theft case in the United States would be cleared by arrests.
Formula used:
If E represents any event and E¯ represents the complement of event E, then the probability of complement event is,
P(E¯)=1−P(E)
Calculation:
Let, event E denote an automobile theft case from 2016 in the United States would be cleared by arrests.
And, event E¯ denotes an automobile theft case in the United States would not be cleared by an arrest.
Since, 13.3% probability that an automobile theft in the United States would be cleared by arrests, so P(E)=13.3%=0.133
Using the formula for probability of complement of an event, P(E¯)=1−P(E).
Hence, P(E¯)=1−0.133.
⇒P(E¯)=0.867
Therefore, the probability that an automobile theft case from 2016 in the United States was not cleared by an arrest is 0.867.
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