To determine which car insurance plan is most likely to save Gareth the most money based on expected value, we need to consider both the deductible of each plan and the total premium cost. We aim to calculate the total expected cost for each plan and select the one with the lowest expected cost.
1. Plan A
- Deductible: [tex]$300
- Premium Total: $[/tex]756
- Probability of Collision: 15%
Expected collision cost:
[tex]\[
0.15 \times 300 = 45
\][/tex]
Total expected cost for Plan A:
[tex]\[
45 + 756 = 801
\][/tex]
2. Plan B
- Deductible: [tex]$500
- Premium Total: $[/tex]655
- Probability of Collision: 15%
Expected collision cost:
[tex]\[
0.15 \times 500 = 75
\][/tex]
Total expected cost for Plan B:
[tex]\[
75 + 655 = 730
\][/tex]
3. Plan C
- Deductible: [tex]$1,000
- Premium Total: $[/tex]534
- Probability of Collision: 15%
Expected collision cost:
[tex]\[
0.15 \times 1000 = 150
\][/tex]
Total expected cost for Plan C:
[tex]\[
150 + 534 = 684
\][/tex]
4. Plan D
- Deductible: [tex]$2,500
- Premium Total: $[/tex]412
- Probability of Collision: 15%
Expected collision cost:
[tex]\[
0.15 \times 2500 = 375
\][/tex]
Total expected cost for Plan D:
[tex]\[
375 + 412 = 787
\][/tex]
Comparing the total expected costs:
- Plan A: [tex]$801
- Plan B: $[/tex]730
- Plan C: [tex]$684
- Plan D: $[/tex]787
The plan with the lowest expected cost is Plan C with a total expected cost of $684.
Therefore, the correct answer is:
C. plan C
