Question

Question: What is the expected value of a prediction with three possible outcomes with the following probabilities: $50: 20% $25: 50% ($25): 30% Please show any math or formulas you use. Answer posibilities are: a. $16.67 b. $25 c. $15 d. $30

What is the expected value of a prediction with three possible outcomes with the following probabilities:

$50: 20%

$25: 50%

($25): 30%

Please show any math or formulas you use.

Answer posibilities are:

a. $16.67

b. $25

c. $15

d. $30

Answer 1

The expected value of a prediction with the given probabilities and outcomes is calculated by multiplying each outcome by its probability and summing the results. The calculated expected value in this scenario is $15.

Step-by-step explanation:

To find the expected value of a prediction with three possible outcomes, you multiply each outcome by its respective probability and sum the results. The formula for expected value (E[X]) is:

E[X] = (Outcome 1 × Probability 1) + (Outcome 2 × Probability 2) + (Outcome 3 × Probability 3)

In this case, the outcomes and probabilities are:

• $50 with a 20% chance (0.20)
• $25 with a 50% chance (0.50)
• -$25 with a 30% chance (0.30) - Note that this is a loss, hence the negative sign

Applying the values:
E[X] = ($50 × 0.20) + ($25 × 0.50) + (-$25 × 0.30)

E[X] = $10 + $12.50 - $7.50

E[X] = $15
Therefore, the correct answer is c. $15.