What is the expected total cost of getting the engineering degree until he is actually getting one with the following details when the risk is taking account to the expected total cost?
Notes: ABC college's engineering overall graduation rate is 50 percentage, that is everyone had uniform chance of graduating and the total cost for the student who are able to graduate is 200000 dollars in case he/she is getting it in one times, the average cost for the student who are not able to graduate is 80000 dollars, so the student who are able to getting in the second time will have the cost of 280000 dollars and so on.
My work is that the answer will be (1/2) (200000 + 80000 x 0) + 1/4(200000 +80000 x 1) + 1/8(200000 + 80000 x 2)+... is that correct?
This question sounds too simple with a feeling that just a few step could address this, maybe I am too stupid or this problem is too tricky that I couldn't figure it out on my own.
Edit 1: "...the average amount that students spend for each degree earned is greater than 200,000." as mentioned by David K.
Edit 2: The fact is that it is just in this problem that everyone had uniform chance of graduating, that is 50%
Your approach seems correct.
Assuming they can keep enrolling until the end of time, then they will always pay $$80,000n+200,000$$
dollars where $n$ is the amount of times they had to enroll prior to the enrollment in which they actually graduated. Assuming independence and each time they enroll, they will graduate with a $0.5$ probability, we just get an infinite sum
$$\sum_{n=0}^{\infty}(80,000n+200,000)\cdot {0.5^{n+1}}$$
Wolfram alpha says that this converges (fortunately) and gives $280,000$.