# Mathematics for Liberal Arts

You are on a TV show. You have been asked to either play a dice game five times or accept a \$50 bill. The dice game works like this:

If you roll a 1, 2 or 3, you win \$46.

If you roll a 4 or 5, you lose \$22.

If you roll a 6, you lose \$85.

Should you play the game? Use expected values and decision theory to justify your answer. (Round the answer to the nearest cent.)

1. 👍
2. 👎
3. 👁
1. The expected winning per game is
(1/2)*46 - (1/3)*22 - (1/6)*85

If that is positive, play the game

1. 👍
2. 👎
2. Take the \$50 and quit.

(Each game as outlined by drwls has an expected value of \$1.50.
You are playing it 5 times, so the expected return is \$7.50.
Your choice was to either accept \$50 or play the game)

1. 👍
2. 👎
3. Reiny is correct. I assumed you were betting your own money. I didn't read all the question.

1. 👍
2. 👎

## Similar Questions

1. ### Probability and statistics

A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win \$5. If you roll a 5, 6, 7, 8, or 9 you lose \$5. Find the expected value you win (or lose) per game.

2. ### Math,set

In a group of 120 students, 72 play chess, 65 play Scrabble and 53 play dice if 35 play both chess and Scrabble, 30 play both chess and dice 21 play both Scrabble and dice and each play at least one of the game. (1) illustrate the

3. ### math

A pair of dice is rolled once. suppose you lose \$9 if the dice sum to 9 and win \$11 if the dice sum to 4 or 6. how much should you win or lose if any other number turns up in order for the game to be fair?

4. ### Math

Another card game. In a new card game, you start with a well-shuffed full deck and draw 3 cards without replacement. If you draw 3 hearts, you win \$50. If you draw 3 black cards, you win \$25. For any other draws, you win nothing.

1. ### Math

A game is played using one dice. If the dice is rolled and shows 1, the player wins \$1; if it shows 2, the player wins \$2; if it shows a 3, the player wins \$3. If the die shows 4,5,or 6 the player wins nothing. a.) If there is a

2. ### math

Suppose someone gives you 8 to 2 odds that you can not roll two even numbers with the roll of two fair dice. This means you win \$8 if you succeed and you lose \$2 if you fail. What is the expected value of this game to you? Should

3. ### Math

Two six-sided dice are rolled at the same time and the numbers showing are observed. Find the following. a. P(sum=6) (1,6), (6,1) 1/36+1/36=2/36 b. P(sum=3) =1/36 c. P(sum is an odd number) 30/36 d. P(the two dice show same

4. ### math help!

A lottery game asks you to pick 5 numbers from the set 1, 2, 3, ... , 29, 30. How many ways are there to play this lottery game? (Assume that this is a game where the order of your picks does NOT matter.) A) 27,405 B) 84,825 C)

1. ### math

A game is defined by the rules that two dice are rolled and the player wins varying amounts depending on the sum of the two dice rolled based on the following table: Sum 2 3 4 5 6 7 8 9 10 11 12 Winnings \$10 \$9 \$8 \$7 \$6 \$5 \$6 \$7

2. ### data management gr.12

A game is defined by the rules that the die is rolled and the player wins varying amounts depending on the number on the upper face according to the following table: sum 1 2 3 4 5 6 Winnings \$10 \$9 \$8 \$7 \$6 \$5 The cost to play the

3. ### math

Phil rolls 6 fair 6-sided dice. What is the probability that at least two dice show the same number?

4. ### English

1. He is good at playing billiards. 2. He is good in playing the billiards. (Can we use 'in' instead of 'at'?) 3. It's the first play-off game, and I'll be the catcher. (What is the meaning of 'the first play-off game'?) 4. I am