Math Problem Statement
The annual premium for a
$5 comma 0005,000
insurance policy against the theft of a painting is
$300300.
If the (empirical) probability that the painting will be stolen during the year is
- 03.03,
what is your expected return from the insurance company if you take out this insurance?
Question content area bottom
Part 1
Let X be the random variable for the amount of money received from the insurance company in the given year.
E(X)equals=enter your response here
dollars
Solution
To find the expected return from the insurance company, we need to calculate the expected value of the random variable , which represents the amount of money received from the insurance company.
Here, can take on two values:
- if the painting is not stolen.
- if the painting is stolen.
The probability that the painting will be stolen during the year is given as 0.03, and the probability that it will not be stolen is .
The expected value is calculated as follows:
Thus, the expected return from the insurance company is .
If you have any questions or want more details, let me know. Here are 5 related questions you might ask:
- How do you calculate expected value in probability?
- What is the significance of expected value in insurance?
- Can you explain other examples of expected value in real-life scenarios?
- How does probability affect insurance premiums?
- What is the difference between empirical and theoretical probability?
Tip: Always verify the given probabilities and conditions to ensure accurate calculations in probability-related problems.
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Math Problem Analysis
Mathematical Concepts
Probability
Expected Value
Formulas
Expected value formula E(X) = ∑ (x * P(X=x))
Theorems
-
Suitable Grade Level
Advanced High School
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