You are in business and you are given two opportunities. The first you will have to invest $5,000 but you could earn $25,000 less your initial investment. The second you only have to invest $2000 but then you will earn $10,000 less your investment. The probability of getting the $25,000 opportunity is 3/10 while the probability of getting the $10000 opportunity is 2/5. Which should you choose based on expected values?

Question

You are in business and you are given two opportunities. The first you will have to invest $5,000 but you could earn $25,000 less your initial investment. The second you only have to invest $2000 but then you will earn $10,000 less your investment. The probability of getting the $25,000 opportunity is 3/10 while the probability of getting the $10000 opportunity is 2/5. Which should you choose based on expected values?

Answer 1

To determine which opportunity you should choose based on expected values, you need to calculate the expected value (EV) for each option.

The expected value is calculated by multiplying the potential outcome by its respective probability and summing all the possible outcomes. In this case, there are two possible outcomes: earning $25,000 or earning $10,000.

For the first option:
- Earning $25,000 less the initial investment of $5,000: $25,000 - $5,000 = $20,000
- Probability of getting the $25,000 opportunity: 3/10

For the second option:
- Earning $10,000 less the initial investment of $2,000: $10,000 - $2,000 = $8,000
- Probability of getting the $10,000 opportunity: 2/5

Now, let's calculate the expected value for each option:

Expected value for the first option:
EV = ($20,000) * (3/10) = $6,000

Expected value for the second option:
EV = ($8,000) * (2/5) = $3,200

Based on their expected values, the first option has an expected value of $6,000, while the second option has an expected value of $3,200. Therefore, you should choose the first option, which is to invest $5,000 for a chance to earn $25,000 less your initial investment.