Question

An investment has a 20% chance of losing $20, a 30% chance of making $10, a 40% chance of making $20, and a 10% chance of making $100. What is the expected value of the investment?

A. -$3
B. $5
C. $12
D. $17
E. $29

Answer 1

The correct answer is option D. To find the expected value of the investment, each outcome's value was multiplied by its probability, and all outcomes were summed together. The result is a $17 expected value, corresponding to option D.

Step-by-step explanation:

The student asked for the expected value of an investment with a given set of probabilities and outcomes. To calculate this, we multiply each outcome by its probability and sum the results.

1. Multiply the profit/loss by its respective probability:
   
   - $20 with a 20% chance: -20 x 0.20 = -4
   
   - $10 with a 30% chance: 10 x 0.30 = 3
   
   - $20 with a 40% chance: 20 x 0.40 = 8
   
   - $100 with a 10% chance: 100 x 0.10 = 10
2. Sum the expected values of all outcomes:
   
   -4 + 3 + 8 + 10 = 17

Therefore, the expected value of the investment is $17, which corresponds to option D.