Question

2. An insurance company has information that 93% of its auto policy holders carry collision coverage or unsecured motorist coverage on their policies. Eighty percent of the policy holders carry collision coverage, and 60% have unsecured motorist coverage.
i. What percentage of these policy holders carry both collision and unsecured motorist coverage?
ii. What percentage of these policy holders carry collision but not unsecured motorist coverage?

Answer 1

Answer:

47%  carry both collision and unsecured motorist coverage.

33%  carry collision but not unsecured motorist coverage.

Step-by-step explanation:

Let 100 be the number of all auto policy holders.

An insurance company has information that 93% of its auto policy holders carry collision coverage or unsecured motorist coverage on their policies. In your case, 93 of all auto policy holders carry collision coverage or unsecured motorist coverage on their policies.

80% of the policy holders carry collision coverage, so 80 of all auto policy holders carry collision coverage.

60% have unsecured motorist coverage, so 60 of all auto policy holders have unsecured motorist coverage.

Let x be the number of all policy holders which carry both collision and unsecured motorist coverage.

Then

• 80 - x carry only collision coverage;
• 60 - x have only unsecured motorist coverage.

Calculate the number of those, who carry collision coverage or unsecured motorist coverage on their policies:

$x+(80-x)+(60-x)=x+80-x+60-x=140-x$

This is exactly 93 people, so

$140-x=93\\ \\x=140-93\\ \\x=47$

47 of 100 is 47%, thus 47% of all policy holders carry both collision and unsecured motorist coverage.

$80-47=33$ carry only collision coverage that is 33%.