<h3>
Answer: 8.50</h3>
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Explanation:
Ignore the rows that are labeled "stock ABC" and "stock MNO".
We only focus on the top row (gains and losses) and the "stock JKL" row.
Multiply each gain or loss with its corresponding probability in decimal form. Use negative values to represent a loss
- -25*0.15 = -3.75
- 5*0.65 = 3.25
- 45*0.20 = 9
Add up those results to get the final answer: -3.75+3.25+9 = 8.50
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Here's another way to get the answer.
Let's say you had a 10 by 10 grid of graph paper.
- Shade exactly 15 tiny squares in red to represent a loss of $25 (note that 15/100 = 15%)
- Shade exactly 65 squares in blue to represent a gain of $5 (65/100 = 65%)
- Shade the remaining 20 squares in green to represent a gain of $45
This can be thought of as like a dart board. Imagine throwing 1000 darts at this grid (maybe do so blindfolded to give each square an equal chance; if you land outside the grid then re-throw the dart). Theoretically, the probability of landing in the red area is 15/100 = 0.15, so we expect about 1000*0.15 = 150 darts will land there out of the 1000 thrown total. Each of those 150 darts in the red area represents a loss of $25. So we have a loss of 150*25 = 3750 dollars. We'll write this as -3750.
We also expect 0.65*1000 = 650 darts to have a gain of $5. That means 650*5 = 3250 is earned here. Furthermore, 0.20*1000 = 200 darts land in the green squares to get us $45 per attempt. So that's another 45*200 = 9000 dollars.
Overall, we would get -3750+3250+9000 = 8500 in profit.
Divide this over the 1000 dart throws and we end up with an expected value of 8500/1000 = 8.50
Keep in mind that this dart game or thought experiment is depending on theoretical probabilities. If you actually do this game, then your empirical probabilities will likely differ slightly from the theoretical values. However, the more trials you conduct, the closer your empirical probabilities should get to the theoretical ones.
