Question

Jared is looking to buy car insurance. The first policy costs $750 for the upcoming year and is worth $16,500 if he gets in a collision. He estimates an 8% chance of getting into a car accident for that year. What is the expected value of buying this insurance policy?

a) $1,260
b) $1,320
c) $1,380
d) $1,440

Answer 1

The expected value of the insurance payout, not accounting for the cost of the policy, is option (b) $1,320, calculated as 8% of the $16,500 collision coverage.

Step-by-step explanation:

The student is asking about the expected value of an insurance policy. To calculate this, we consider the cost of the policy and the potential benefit in the event of a collision, alongside the probability of that event.

The policy costs Jared $750 and pays out $16,500 in the event of a collision. Jared estimates there is an 8% chance he will get into a car accident. We calculate the expected value (EV) using the formula: EV = (Probability of Collision × Payout in Event of Collision) - Cost of Policy.

Plugging in the values: EV = (0.08 × $16,500) - $750 = $1,320 - $750 = $570.

However, the offered options suggest we are looking for the expected payout in case of collision only, not subtracting the insurance cost. So we calculate as follows: EV = (0.08 × $16,500) which equals $1,320.