Comparing Insurance with Expected Value
Insurance companies show a lot of plans and try to lure customers to buy them. Not all the plans are beneficial to customers. One such case is medical insurance. A lot of insurance companies, to make more profit, make attractive schemes that are not beneficial in the long term. In such cases, it becomes essential to use the expectations and calculate the expected medical costs. Such methods usually help in differentiating between plans and making a wise decision about medical insurance. To get a better idea about this case, let’s consider the example given below.
Example: Vasu wants to buy a medical insurance plan, but he is confused between plan A and plan B.
Plan A: This is a low deductible plan, he will have to pay the first 10,000 rupees of any medical costs. Additionally, to cover the plan, he will have to pay Rs 80,000 per year.
Plan B: This is a high-deductible plan, he will have to pay the first 25,000 rupees of any medical costs. Additionally, to cover the plan, he will have to pay Rs 60,000 per year.
Find the expected cost for both plans and help Vasu decide. A table is given which gives the stats about the probability of these medical expenses.
| Medical Cost | Probability |
|---|---|
| Rs 0 | 30 % |
| Rs 10000 | 25 % |
| Rs 40,000 | 20 % |
| Rs 70,000 | 20 % |
| Rs 1,50,000 | 5 % |
Solution:
Let random variable X define the expected cost,
Expected value for Plan A:
E(X) = 80,000 + 0 (0.3) + 10000(0.25) + 10000(0.2) + 10000(0.2) + 10000(0.05)
⇒ E(X) = 80,000 + 2500 + 2000 + 2000 + 500
⇒ E(X) = 87000
Expected value for plan B:
E(X) = 60,000 + 0 (0.3) + 10000(0.25) + 25000(0.2) + 25000(0.2) + 25000(0.05)
⇒ E(X) = 60,000 + 2500 + 5000 + 5000 + 1250
⇒ E(X) = 73,750
Expected expenses are most in plan A. Thus, Vasu should take plan B.
Expected Value
Expected Value: Random variables are the functions that assign a probability to some outcomes in the sample space. They are very useful in the analysis of real-life random experiments which become complex. These variables take some outcomes from a sample space as input and assign some real numbers to it. The expectation is an important part of random variable analysis. It gives the average output of the random variable.
Table of Content
- What is Expected Value?
- Random Variables and Expectations
- Expectation
- Expected Value
- Properties of Expected Value
- Term Life Insurance and Death Probability
- Getting Data from Expected Value
- Expected Profit from Lottery Ticket
- Expected Value while Fishing
- Comparing Insurance with Expected Value
- Expected Value – Solved Examples