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11 A Fair Game
Basic Concepts A Fair Game
In a die game, you can get a cash prize that is 100 times the
number rolled after paying an entry fee. Since the possible
outcomes of rolling a die are 1, 2, 3, 4, 5, and 6, the cash prize
can be $100, $200, $300, $400, $500, or $600. The probability
of rolling each number from 1 to 6 is the same, and the average cash prize
you get is ($100 $200 $300 $400 $500 $600) 6 $350. Therefore,
the entry fee should be $350 to be fair. When the entry fee is equal to the
money earned from the game, it is called a fair game.
Example The spinner below is labeled from 1 to 8. Each player will receive a
cash prize of 1,000 times the number spun, as shown in the box.
How much money should each player pay to spin once in order for
this game to be fair?
81 Number spun: 1 $1,000
72 Number spun: 2 $2,000
63 Number spun: 3 $3,000
54
Class Notes
There are possible outcomes when spinning the numbers 1, 2, 3, 4, 5, 6, 7, and 8,
and the cash prize is $1,000, $2,000, $3,000, , , , , or
in each case.
The probability of spinning each number from 1 to 8 is the same, and the average cash prize is
($1,000 $2,000 $3,000 $4,000 $5,000 $6,000 $7,000 $8,000) .
Therefore, should be the entry fee to have a fair game.
94 NUMINO Challenge D2
Basic Concepts A Fair Game
In a die game, you can get a cash prize that is 100 times the
number rolled after paying an entry fee. Since the possible
outcomes of rolling a die are 1, 2, 3, 4, 5, and 6, the cash prize
can be $100, $200, $300, $400, $500, or $600. The probability
of rolling each number from 1 to 6 is the same, and the average cash prize
you get is ($100 $200 $300 $400 $500 $600) 6 $350. Therefore,
the entry fee should be $350 to be fair. When the entry fee is equal to the
money earned from the game, it is called a fair game.
Example The spinner below is labeled from 1 to 8. Each player will receive a
cash prize of 1,000 times the number spun, as shown in the box.
How much money should each player pay to spin once in order for
this game to be fair?
81 Number spun: 1 $1,000
72 Number spun: 2 $2,000
63 Number spun: 3 $3,000
54
Class Notes
There are possible outcomes when spinning the numbers 1, 2, 3, 4, 5, 6, 7, and 8,
and the cash prize is $1,000, $2,000, $3,000, , , , , or
in each case.
The probability of spinning each number from 1 to 8 is the same, and the average cash prize is
($1,000 $2,000 $3,000 $4,000 $5,000 $6,000 $7,000 $8,000) .
Therefore, should be the entry fee to have a fair game.
94 NUMINO Challenge D2
