**Expected Value Calculation for an Insurance Policy****Problem Statement:**Based on historical data, an insurance company estimates that a particular customer has a 2.7% likelihood of having an accident in the next year, with the average insurance payout being $1900.If the company charges this customer an annual premium of $200, what is the company's expected value of this insurance policy?**Explanation:**The expected value (EV) of an insurance policy from the company's perspective can be calculated considering both the premium received and the potential payout in case of an accident.**Step-by-Step Calculation:**1. **Identify Probabilities and Payouts:** - Probability of an accident (P_accident): 2.7% or 0.027 - Probability of no accident (P_no_accident): 1 - P_accident = 1 - 0.027 = 0.973 - Average insurance payout if an accident occurs: $1900 - Annual premium paid by the customer: $2002. **Calculate Expected Payoff from Accidents:** - If an accident happens, the company pays $1900. - Expected payout due to an accident: P_accident * payout = 0.027 * $1900 = $51.303. **Calculate Expected Premiums Collected:** - Premium is collected regardless of whether an accident occurs. - Expected premium collected: P_accident * $200 + P_no_accident * $200 = $2004. **Calculate Expected Value (EV):** - The company's expected profit/loss from the policy can be calculated as follows: EV = Expected Premiums - Expected Payouts EV = $200 - $51.30 EV = $148.70**Conclusion:**The company's expected value of this insurance policy is $148.70. This means, on average, the company expects to make a profit of $148.70 per year per customer from this type of policy.

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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