select the correct answer. gareth is choosing a car insurance plan. based on his driving history and the…

select the correct answer. gareth is choosing a car insurance plan. based on his driving history and the traffic where he lives, gareth estimates that there is a 15% chance he 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 gareth the most money, based on expected value?\n| plan | a | b | c | d |\n|--|--|--|--|--|--|\n| deductible | $300 | $500 | $1,000 | $2,500 |\n| collision | $516 | $445 | $350 | $288 |\n| comprehensive | $240 | $210 | $184 | $124 |\n| premium total | $756 | $655 | $534 | $412 |

select the correct answer. gareth is choosing a car insurance plan. based on his driving history and the traffic where he lives, gareth estimates that there is a 15% chance he 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 gareth the most money, based on expected value?\n| plan | a | b | c | d |\n|--|--|--|--|--|--|\n| deductible | $300 | $500 | $1,000 | $2,500 |\n| collision | $516 | $445 | $350 | $288 |\n| comprehensive | $240 | $210 | $184 | $124 |\n| premium total | $756 | $655 | $534 | $412 |

Answer

Explanation:

Step1: Calculate expected out - of - pocket cost for each plan

The expected out - of - pocket cost for a plan is the sum of the expected deductible (probability of a collision times deductible) and the premium. The probability of a collision is 0.15. For plan A: The expected deductible is $0.15\times300 = 45$. The premium is $756$. So the total expected out - of - pocket cost is $45 + 756=801$. For plan B: The expected deductible is $0.15\times500 = 75$. The premium is $655$. So the total expected out - of - pocket cost is $75+655 = 730$. For plan C: The expected deductible is $0.15\times1000 = 150$. The premium is $534$. So the total expected out - of - pocket cost is $150 + 534=684$. For plan D: The expected deductible is $0.15\times2500=375$. The premium is $412$. So the total expected out - of - pocket cost is $375 + 412 = 787$.

Answer:

C. plan C