Answer:
i) The percentage of both collision and unsecured is 47%
ii) The percentage of carry collision but not unsecured is 33%
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%