Expected Value

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Show your work for each problem.

1.
What does the expected value of a random experiment represent?
1. a)The long-run average outcome
2. b)The minimum possible outcome
3. c)The maximum possible outcome
4. d)The most likely outcome
2.
What is the expected value when flipping a fair coin where heads = 1 and tails = 0?
3.
A fair six-sided die is rolled. What is the expected value?
1. a)3
2. b)3.5
3. c)4
4. d)3.25
4.
A spinner has 4 equal sections numbered 2, 4, 6, and 8. Find the expected value.
5.
A biased coin has a 60% chance of heads (win 3 euros) and 40% chance of tails (lose 2 euros). What is the expected value?
6.
A game costs 5 euros to play. You roll a die and win 12 euros if you roll a 6, otherwise you win nothing. What is the expected profit?
1. a)0 euros
2. b)-3 euros
3. c)-2 euros
4. d)2 euros
7.
A lottery ticket costs 2 euros. There's a 5% chance of winning 20 euros and a 95% chance of winning nothing. Calculate the expected profit.
8.
If a game has an expected value of -2 euros, what does this mean?
1. a)You will always lose 2 euros
2. b)You can never win
3. c)On average, you lose 2 euros per game
4. d)The game costs 2 euros to play
9.
A spinner has 3 sections: red (50%), blue (30%), yellow (20%). Red wins 4 euros, blue wins 2 euros, yellow loses 5 euros. What is the expected value?
10.
An insurance company charges 200 euros per year. 3% of customers file claims averaging 4000 euros. What is the expected profit per customer?
11.
In European roulette, betting 10 euros on a single number pays 350 euros if you win (35:1 odds). There are 37 numbers. What is the expected value of this bet?
12.
A game show offers: keep 1000 euros OR flip a coin where heads wins 2500 euros and tails wins 0 euros. Which has higher expected value and by how much?
13.
Investment A: 40% chance of +30%, 60% chance of -10%. Investment B: 80% chance of +10%, 20% chance of +5%. Which has higher expected return?
1. a)Investment A (9%)
2. b)They are equal
3. c)Investment A (6%)
4. d)Investment B (9%)
14.
A company manufactures products. 2% are defective and cost 500 euros each to replace. Good products earn 20 euros profit. What is the expected profit per product?
15.
Why can't you expect to roll 3.5 on a single die roll, even though the expected value is 3.5?
1. a)The expected value is wrong
2. b)3.5 is not a possible outcome on a die
3. c)You need to roll twice
4. d)The die is unfair
16.
Two dice are rolled and their sum is recorded. What is the expected value of the sum?