8/16 MATH 131-Unit 2 Class Activity 2 Example 2i Dan is pricing car insurance fr

Question

8/16 MATH 131-Unit 2 Class Activity 2 Example 2i Dan is pricing car insurance from a new company that only pays out at 3 levels: total, major accident and fender bender. His car is valued at $20,000. After reviewing his application, his insurance company assigned him to a group with the probabilities listed below. These values are used to figure the value the company must charge to cover their payouts. If the company charges a $200 service fee, what will be his annual premium? x P(x) x, payoutP(x) 0.010 0.020 0.090 20,000 total 10,000 major 2000 fender bender 0 no accident Try it yourself: If you were buying a similar policy with your car also valued at $20,000, what probabilities for payout do you believe would be assigned. What should be your annual premium? x, payout P(x) x P(x) 20,000 10,000 2,000 total major fender bender no accident

Explanation / Answer

Example 2

Here as we know sum of all probabilites is 1.

so,

P(Total) + P(major) + P(fender bender) + P(no accident) = 1

0.010 + 0.020 + 0.090 + P(no accident) = 1

P(no accident) = 0.88

Total expected payout = $ 580

Servie fee = $ 200

Total premium Charged = $ 580 + $ 200 = $ 780

For my car, i will assigned probabily as below.

My annual premium would be $ 900 + $ 200 = $1100  

x(Payout) P(x) xP(x) 20000 0.01 200 10000 0.02 200 2000 0.09 180 0 0.88 0 Sum 1 580

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