An Automobile Insurance Company Estimates the Following Loss Probabilities for the Nextyear

question 236

Essay

An automobile insurance company estimates the following loss probabilities for the nextyear on a $25,000 sports car:
$$\begin{array} { l l } \text { Total loss: } & 0.001 \\50 \% \text { loss: } & 0.01 \\25 \% \text { loss: } & 0.05 \\10 \% \text { loss: } & 0.10 \\\text { No loss: } & 0.839\end{array}$$ Assuming the company will sell only a $500 deductible policy for this model (i.e., the owner covers the first $500 damage), how much annual premium should the company charge in order to average $565 profit per policy sold?

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Definitions:

Anger

A strong emotional state that typically arises from feelings of displeasure, frustration, or antagonism towards someone or something.

Fear

An emotional response triggered by perceived threats, leading to a fight-or-flight reaction.

Basic Emotions

Fundamental emotions that are universally recognized and expressed, such as happiness, sadness, fear, disgust, anger, and surprise.

Emotional Response

A reaction involving feelings that occurs as a result of an external stimulus, internal thoughts, or memories.