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Chapter 4: Problem 148

An insurance company has information that \(93 \%\) of its auto policy holders carry collision coverage or uninsured motorist coverage on their policies. Eighty percent of the policy holders carry collision coverage, and \(60 \%\) have uninsured motorist coverage. a. What percentage of these policy holders carry both collision and uninsured motorist coverage? b. What percentage of these policy holders carry neither collision nor uninsured motorist coverage? c. What percentage of these policy holders carry collision but not uninsured motorist coverage?

Short Answer

Expert verified
a) The percentage of policy holders who carry both collision and uninsured motorist coverage is \(80 + 60 - 93 = 47% \). b) The percentage of policy holders who carry neither collision nor uninsured is \(100 - 93 = 7% \). c) The percentage of policy holders who carry collision but not uninsured motorist coverage is \(80 - 47 = 33% \).

Step by step solution

01

Calculate the percentage of both collision and uninsured motorist coverage

To find what percentage of policy holders have both collision and uninsured motorist coverage, you need to sum the collision coverage holders (80 percent) and the uninsured motorist coverage holders (60 percent), then subtract from the total coverage holders (93 percent). This is based on the Inclusion鈥揈xclusion Principle.\[bothCoverage = 80 + 60 - 93\]
02

Calculate the percentage of neither collision nor uninsured motorist coverage

To find the percentage of policy holders that have neither collision nor uninsured motorist coverage, you subtract the total coverage holders from 100 percent, the total population percentage. \[neitherCoverage = 100 - 93\]
03

Calculate the percentage of collision but not uninsured motorist coverage

To find the percentage of policy holders that carry collision but not uninsured motorist coverage, you subtract the percentage of both coverages from the total percentage of collision coverage. \[collisionOnly = 80 - bothCoverage\]

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