question archive Brenda is choosing a car insurance plan
Brenda is choosing a car insurance plan
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Brenda is choosing a car insurance plan. Based on her driving history and traffic where she lives, Brenda estimates that there is a 20% chance she will have a car collision this year. In each plan, the insurance will cover the full cost of the collision after the deductible is paid. Which of the plans detailed in the table is most likely to save Brenda the most money. Based on expected value?
|
Plan |
Deductible |
Collision |
comprehensive |
Premium total |
|
A |
$300 |
$500 |
$234 |
$734 |
|
B |
$500 |
$430 |
$212 |
$642 |
|
C |
$1,000 |
$340 |
$175 |
$515 |
|
d |
$2,500 |
$278 |
$127 |
$405 |
- Plan a
- Plan B
- Plan c
- Plan D
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The answer is alternative c. Plan C
Step-by-step explanation
For each of the options, Brenda will have to pay the option's Premium and there is a 20% chance that she will have to pay the deductible (in case of a collision). The expected cost for each plan is:
?E(A)=734+0.20∗300E(A)=$794?
?E(B)=642+0.20∗500E(B)=$742?
?E(C)=515+0.20∗1,000E(C)=$715?
?E(D)=405+0.20∗2,500E(D)=$905?
Therefore, plan C presents the lowest expected cost and is the one that Brenda should choose.
