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 game is $7.00
a) what can a player expect to win by playing this game?
b) what would be a fair value to pay to play this game?
Thanks.
Expected value,
E[x]=Σpixi
Now complete the table below
sum P(sum) X(sum)
1 1/6 $10
2 1/6 $9
3 1/6 $8
4 1/6 $7
5 1/6 $6
6 1/6 $5
E[X]=ΣP(sum)X(sum)
=(10+9+8+7+6+5)/6
=45/6
=7.5
Cost to play the game = 7.0
Expected winning = 7.5-7.0=0.50
I leave it to you to find the fair price to play the game.
Game Equipment: 1 game board, 1 deck of playing cards, 25 playing pieces (5 each of 5 colors).
To Start: Each player chooses a color and places the pieces of that color on the matching HOME circle. One player shuffles the deck and places it face down on the space marked CARDS. Select a player to play first. The winner of the game goes first in the next.
The Object of the Game: The player who first moves all of her pieces from her HOME to her GOAL, of the same color wins.
1. Which of the following is correct according to the board games rules?
a. the player who shuffles the pack of cards gets to go first.
b. game pieces must ne moved to the home circle to win.
c.there are 25 playing cards in the deck.
d. the maximum noumber of players is five.
I chose D
2. Which of the following is the purpose of using all capitalized letters in the rules?
a. to emphasize placement of the playing pieces.
b. to indicate text from the game board.
c. to emphasize important rules.
d. to indicate the title of certain playing cards.
I chose B
To calculate the expected winnings, we need to multiply each possible outcome by its corresponding probability and then sum them up.
a) To find out what a player can expect to win by playing this game, we first need to find the probability of each outcome. Since the die has 6 sides, each number from 1 to 6 has an equal probability of 1/6.
Using the given table of winnings, we multiply each winning amount by its probability as follows:
Winning amount:
$10 * (1/6) = $10/6
$9 * (1/6) = $9/6
$8 * (1/6) = $8/6
$7 * (1/6) = $7/6
$6 * (1/6) = $6/6
$5 * (1/6) = $5/6
Now, let's calculate the expected winnings:
Expected winnings = (10/6) + (9/6) + (8/6) + (7/6) + (6/6) + (5/6)
Expected winnings = 45/6
Dividing numerator and denominator by 3 to simplify:
Expected winnings = 15/2
Therefore, a player can expect to win $15/2 or $7.50 by playing this game.
b) To find a fair value to pay to play this game, we need to calculate the expected winnings and subtract the cost of playing.
Fair value = expected winnings - cost of playing
Fair value = 15/2 - 7
Fair value = 15/2 - 14/2
Fair value = 1/2
Therefore, a fair value to pay to play this game would be $1/2 or 50 cents.