Teresa T.

asked • 12/12/12

Probability and expected value

You are in business and you are given two opportunities. The first you will have to invest $5000 but you could earn $25,000 less your initial investment. The second you only have to invest $2000 but then you will only earn $10,000 less your investment. The probability of getting $25,000 opportunity is 3/10 while the probability of getting $10,000 is 2/5. Which should you choose based on expected values?

2 Answers By Expert Tutors


Ryan Maxwell W. answered • 09/29/19

Master's in Math, 10+ years teaching and tutoring professionally

George P. answered • 12/14/12

Mathematics: High School/Undergrad/Actuarial exam preparation.

Daniel O.

Unless I'm interpreting the question wrong, shouldn't opportunity 1's EV be:

(3/10)*25,000 - 5000 = $2500

and opportunity 2's EV: 

(2/5)*10,000 - 2000 = $4000

Because when opportunity 1 pays off, we get $25000 (but $5000 of that was our initial investment) and when opportunity 2 pays off, we get $10K (but $2k of that was our own)

- that's the way I interpreted the "you could earn $25,000 less your initial investment" and "you will only earn $10,000 less your investment" but maybe I should be reading it as "you get $20,000 for opp. 1 [and $8000 for opp. 2] at the end of the investment", as in the instituition (or whomever) is keeping our initial investment.



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