Question

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 uninsured 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:

i) The percentage of both collision and unsecured is 47%

ii) The percentage of carry collision but not unsecured is 33%

Step-by-step explanation:

* Lets study the meaning of "or" , "and" on probability

- The use of the word "or" means that you are calculating the

  percentage that either event A or event B happened

- The use the word "and" means that both event A and B have

  to happen

* The addition rules is:

# P(A or B) = P(A) + P(B) - P(A and B)

- The union is written as A∪B or “A or B”.  

- The Both is written as A∩B or “A and B”

* Lets solve the question

∵ P(collision) = 80%

∵ P(unsecured) = 60%

∵ P(collision or unsecured) = 93%

i)

- To find P(collision and unsecured) use the rule:

  P(A or B) = P(A) + P(B) - P(A and B)

∴ P(collision or unsecured) = P(collision) + P(unsecured) - P(collision

   and unsecured)

- Substitute the values of P(collision) , P(unsecured) ,

  P(collision or unsecured)  in the rule

∵ 93% = 80% + 60% - P(collision and unsecured)

- Add the like terms

∴ 93% = 140% - P(collision and unsecured)

- Subtract 140% from both sides

∴ 93% - 140% = - P(collision and unsecured)

∴ - 47% = - P(collision and unsecured)

- Multiply both sides by -1

∴ 47% = P(collision and unsecured)

∴ P(collision and unsecured) = 47%

∴ The percentage of both collision and unsecured is 47%

ii)

∵ The percentage of policy holders carry collision is 80%

∵ The percentage of both collision and unsecured is 47%

- The percentage of policy holders carry collision but not unsecured

 is the difference between the collision and the collision and

 unsecured

∴ The percentage of policy holders carry collision but not unsecured

   = 80% - 47% = 33%

∴ The percentage of carry collision but not unsecured is 33%