User: Assume 3 in every 3000 students at the local community college have to quit due to serious health issues. An insurance company offers them ma$12,000 policy for $50 a year. What is the amount the insurance company should expect to make on average on every student that pays?

Question

anonymous · Answer

Each year the company expects to pay out (3)(12000)= $36000
It expects to collect (50)(3000) = $150,000 per year 
the difference is $114000 per year.

anonymous · Answer

Thanks, they said the answer is wrong.

kropot72 · Answer

The probability that a student claims is 3/3000 = 1/1000
The average loss per student is 
$$12000\times\frac{1}{1000}=12\ dollars$$
The income per student is $50.
Therefore the average profit per participating student is 50 - 12 = $38

anonymous · Answer

Did you divide the $114,000 gain by the number of students to get a per student estimate? That gives $38.

kropot72 · Answer

@douglaswinslowcooper Your calculation assumes that every student participates. Although your method can arrive at a correct answer, I believe that mine is more in keeping with the question:
"What is the amount the insurance company should expect to make on average on every student that pays?"