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t Lemonade Insurance Company charge each of Rainie anc break even'? e this contract if she is charged the 'break-even' premium? V ontact if he is charged the 'break-even' premium? Briefly of risk Lemonade Insurance Company faces if they sell inie and Ben?

t Lemonade Insurance Company charge each of Rainie anc break even'? e this contract if she is charged the 'break-even' premium? V ontact if he is charged the 'break-even' premium? Briefly of risk Lemonade Insurance Company faces if they sell inie and Ben?

A First Course in Probability (10th Edition)
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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Answer a, b, and c
### Insurance Premium and Risk Analysis: Educational Scenario #### Scenario Description Suppose Ben owns a $600,000 house and has an 8% chance of experiencing a fire in any given year. Assume as before that the fire will result in a total loss. Suppose the Lemonade Insurance Company offers Rainie and Ben the same insurance contract and charges them the same premium. In other words, they put Rainie and Ben into the same risk pool. #### Questions: a. **What is the probability distribution of total losses for Lemonade Insurance Company if they sell contracts to Rainie and Ben?** b. **What premium must Lemonade Insurance Company charge each of Rainie and Ben if they want to ‘break even’?** c. **Will Rainie purchase this contract if she is charged the ‘break-even’ premium? Will Ben purchase this contract if he is charged the ‘break-even’ premium? Briefly explain your reason.** d. **What is the amount of risk Lemonade Insurance Company faces if they sell contracts to both Rainie and Ben?** ### Discussion: #### a. Probability Distribution of Total Losses Analyzing the probability distribution involves determining the likelihood of various outcomes (e.g., both experiencing a total loss, only one experiencing a total loss, or neither experiencing a total loss) and associated costs. #### b. Break-Even Premium Calculation To break even, the insurance company would calculate the expected payout for each policyholder and set a premium that covers these expected costs plus any administrative expenses. #### c. Purchase Decision Analysis Evaluating whether Rainie and Ben would find the break-even premium acceptable involves comparing the premium to their perceived risk and value of the insurance. #### d. Amount of Risk Assessing the risk the insurance company faces includes evaluating the variance in potential total losses and financial implications. ### Detailed Explanations 1. **Probability Distribution of Losses**: - The probability of neither experiencing a total loss. - The probability of only Rainie experiencing a total loss. - The probability of only Ben experiencing a total loss. - The probability of both experiencing total losses. 2. **Premium Calculation**: - Calculation based on the expected cost of claims from Rainie and Ben considering their risk levels. 3. **Consumer Decision Analysis**: - Evaluation sheet comparing risk perception and the premium rate. 4. **Risk Assessment for Insurance Company**: - Statistical analysis on the potential financial exposure from
Transcribed Image Text:### Insurance Premium and Risk Analysis: Educational Scenario #### Scenario Description Suppose Ben owns a $600,000 house and has an 8% chance of experiencing a fire in any given year. Assume as before that the fire will result in a total loss. Suppose the Lemonade Insurance Company offers Rainie and Ben the same insurance contract and charges them the same premium. In other words, they put Rainie and Ben into the same risk pool. #### Questions: a. **What is the probability distribution of total losses for Lemonade Insurance Company if they sell contracts to Rainie and Ben?** b. **What premium must Lemonade Insurance Company charge each of Rainie and Ben if they want to ‘break even’?** c. **Will Rainie purchase this contract if she is charged the ‘break-even’ premium? Will Ben purchase this contract if he is charged the ‘break-even’ premium? Briefly explain your reason.** d. **What is the amount of risk Lemonade Insurance Company faces if they sell contracts to both Rainie and Ben?** ### Discussion: #### a. Probability Distribution of Total Losses Analyzing the probability distribution involves determining the likelihood of various outcomes (e.g., both experiencing a total loss, only one experiencing a total loss, or neither experiencing a total loss) and associated costs. #### b. Break-Even Premium Calculation To break even, the insurance company would calculate the expected payout for each policyholder and set a premium that covers these expected costs plus any administrative expenses. #### c. Purchase Decision Analysis Evaluating whether Rainie and Ben would find the break-even premium acceptable involves comparing the premium to their perceived risk and value of the insurance. #### d. Amount of Risk Assessing the risk the insurance company faces includes evaluating the variance in potential total losses and financial implications. ### Detailed Explanations 1. **Probability Distribution of Losses**: - The probability of neither experiencing a total loss. - The probability of only Rainie experiencing a total loss. - The probability of only Ben experiencing a total loss. - The probability of both experiencing total losses. 2. **Premium Calculation**: - Calculation based on the expected cost of claims from Rainie and Ben considering their risk levels. 3. **Consumer Decision Analysis**: - Evaluation sheet comparing risk perception and the premium rate. 4. **Risk Assessment for Insurance Company**: - Statistical analysis on the potential financial exposure from
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