Question

Assume 3 in every 1000 students at a local community college have quit due to serious health issues. An insurance company offers them an $8000 policy for $50 a year. What is the amount the insurance company should expect to make on average on every student that pays?

Answer 1

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Below is the solution:

 E(X) = 50*1 - 3*8000/10000 
E(X) = 50 - 24 = $26 per year

Answer 2

Answer: if 3 for every 1000 students quit due serious health issues, then you can see the proportion doing the quotient between this numbers. This is:

3/1000 = 0.003

Then if you choose a random student, you have a 0.003 probability of choosing one who can have a health issue.

and a 0.997 probability to choose a student with no health issues.

Now, the company wins  $50 for the healthy students, and lose ($50 - $8000)  = -$7950 for each student that is sick (because they initially pay the 50$ and latter get the $8000).

Then the insurance company should expect to make in average:

0.997*$50 - 0.003*($7950) = $26

So the company should expect to make 26 dollars per student in a year.