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?
Probability and expected value
Hi Teresa. For two-case probability and expected value type questions like this, we are calculating how much we can expect to make in the future, based on two variables - magnitude of the opportunity and the likelihood that it will occur. For this particular question, we look at the formula for expected value, E[x], given the probability, p(x), of earning x dollars:
E[x] = p(x)*x
For example, if I flipped a fair coin and promised you $20 if a heads came up, you can expect to earn:
E[x]= (.5) * ($20) = $10 (Notice .5 is the probability of a heads facing up)
Now for your example, there is a slight catch; for each opportunity, you are required to invest an initial amount (there is a 100% chance that you pay this initial amount) or E[x]=(1)* (- initial_investment) = - initial_investment (notice the negative sign because you are paying, not earning, this amount).
After calculations, we see E2[x] > E1[x], and we would rather choose Opportunity 2 because it is expected to earn a larger sum of money.