Question

An insurance company has info that 96% of its auto policy holders use collision coverage or uninsured motor coverage. 89% of policy holders use collision coverage while 75% use uninsured motor coverage.

1)What percentage of policy holders dont use either?

2)What percentage of them use both?

3) What percentage use collision but not uninsured motor coverage?

4) What percentage of them use uninsured but not collision coverage?

Answer 1

1)

P(Do not use either) = 1 - P( use collision coverage or uninsured motor coverage)

= 1 - 0.96

= 0.04

= 4%

2)

P( use collision coverage or uninsured motor coverage) = P( use collision coverage) + P(uninsured motor coverage)

- P( use collision coverage and uninsured motor coverage)

0.96 = 0.89 + 0.75 - P( use collision coverage and uninsured motor coverage)

So,

P( use collision coverage and uninsured motor coverage) = 0.89 + 0.75 - 0.96

= 0.68

= 68%

3)

P(Use collision and not uninsured motor coverage) = P(Collision) - P( use collision coverage and uninsured motor coverage)

= 0.89 - 0.68

= 0.21

= 21%

4)

P(use uninsured and not collision coverage) = P(Uninsured) - P( use collision coverage and uninsured motor coverage)

= 0.75 - 0.68

= 0.07

= 7%