Remember, the Key Formula You Need for Expected Value Is

Intermediate Microeconomics

Expected Value Practice

Remember, the key formula you need for expected value is:

In words, the expected value is the sum of the probability times the value; AND the sum of the probabilities must equal 1 (collectively exhaustive.)

Remember the process:

1. What does your answer look like? Is it a number? A dollar figure? A probability?

2. What do you know?

3. Use what you know to get where you need to go!

You can get easily overwhelmed and frustrated if you try to read the problem and figure out the answer in your head in one step. Take a step back, think methodically, and you’ll get it.

Here are your problems:

1. What is the expected value of a random toss of a fair six-sided die?

ANSWER: 3.5

2. What is the expected value of a random toss of an unbalanced six-sided die where the probability of rolling a 4 or a 6 is 30% (each independently) while the probabilities of rolling any other number are equal.

ANSWER: 4.1

Ask yourself: Does it make sense that your expected value in #2 is higher than in #1?

3. Congratulations! You are up for a raise and a promotion. You currently earn $50,000. You have a 25% chance of getting a raise of 10% and a 10% chance of getting promotion with a raise of 50%. What is your expected salary?

ANSWER: .25(50,000*1.1) + .1(50,000*1.5) +.65(50,000) = 53,750

Key: many folks forget the probability of not getting either the raise or the promotion! Remember, options must be collectively exhaustive and so probabilities need to sum to 1

4. You are booking a vacation worth $3,000 and have the option to purchase trip insurance. If there is a 20% chance that your flight will be cancelled because of weather, what is your expected loss? What is the expected value of your trip?

ANSWER: .2(3000) = 600

5. Following from question 4, if there is a 20% chance your flight will be cancelled and you won’t be able to go on your trip at all, and a 30% chance that your flight will be just delayed and you will miss your connection resulting in $1,000 lost value of your trip (e.g. you miss a day) then what is your expected loss? What is the expected value of your trip?

ANSWER: expected loss = .2(3000) + .3(1000) + .5(0 – no loss) = 900

Expected value = .2(0 – no value) + .3(2,000) + .5(3000) = 1,900