Expected Value Word Problems

1.

Multiple Choice

5 mins

1 pt

Given the probability model in the table below, what is the expected value of the random variable?
X 50 20 5
P(X) 0.1 0.3 0.6

14

4.67

5

7.5

2.

Multiple Choice

30 sec

1 pt

If the expected value is negative, are you expected to win?

yes

no

3.

Multiple Choice

1 min

1 pt

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?

$12.50

$5

$7.50

$10

4.

Multiple Choice

1 min

1 pt

Eva flips a coin. If she gets heads, she wins $4. If she gets tails, she loses $3. What is her expected value of a coin flip?

$1

$0.50

-$0.50

$0

5.

Multiple Choice

1 min

1 pt

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise. Is this a fair game?

yes

no

6.

Multiple Choice

1 min

1 pt

Suppose you buy a ticket for $6 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. How much money do you take home (after paying for it)?

$800

-$6.50

-$6

-$5.20

7.

Multiple Choice

3 mins

1 pt

Choose an American household at random. What is the expected number of cars for that household?

1.75

1.84

2.00

2.50

8.

Multiple Choice

5 mins

1 pt

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution. What is the average number of customers that the owner can expect to make a purchase in the first hour of opening?

0.2

1.4

2.0

3.0

9.

Multiple Choice

30 sec

1 pt

The following table shows the probability distribution for the number of children in each family in the town of Crossville. What is the average number of children in this town?

1.9

0.3

2.1

3

10.

Multiple Choice

3 mins

1 pt

You pick a card from a deck. If you get a face card, you win $5. If you get an ace, you win $30 plus an extra $60 for the ace of hearts. For any other card you win nothing. Find the expected value you will win.

$5.00

$3.85

$4.04

$4.62

11.

Multiple Choice

3 mins

1 pt

A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. What is the expected value

$0

-$0.50

$.67

$-1.50

12.

Multiple Choice

1 min

1 pt

One option in the game of roulette is to bet $6 on red. (There are 18 red compartments, 18 black compartments and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $6 you paid to play and you are awarded an additional $6. If the ball does not land on red, you win nothing and you lose your $6 bet. Find the expected payback (on average) for this game if you bet on red.

-$5.54

-$0.32

-$4.48

13.

Multiple Choice

5 mins

1 pt

A child asks his parents for some money. The parents make the following offers.
Father’s offer: The child fl ips a coin. If the coin lands heads up, the father will give the child $20. If the coin lands tails up, the father will give the child nothing.
Mother’s offer: The child rolls a 6-sided die. The mother will give the child $3 for each dot on the upside of the die.
Which offer has the greater expected value?

Mother's Offer

Father's Offer

14.

Multiple Choice

30 sec

1 pt

If the expected value is positive, are you expected to win?

yes

no

15.

Multiple Choice

5 mins

1 pt

Number of Thunderstorms during August
Number of Storms 0 1 2 3
Probability 0.2 0.2 0.4 0.2
How many storms should we expect in August?

1.8

2.0

1.6

2.2

16.

Multiple Choice

2 mins

1 pt

The world famous gambler from Philadelphia, Señor Rick, proposes the following game of chance. You roll a fair die. If you roll a 1, then Señor Rick pays you $25. If you roll a 2, Señor Rick pays you $5. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must pay Señor Rick $10, and if you roll a 6, you must pay Señor Rick $15. Is Señor Rick proposing a fair game?

No. You win $0.83 in the long run.

Yes, neither of you wins or loses in the long run.

No. You lose $0.83 in the long run.

Yes, the expected value is positive.

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