SOLUTION: A game is played using 1 dice. If the dice is rolled and shows a 5, the player wins $5.00. If the dice is rolled and shows a 4, the player wins $4.00. If the dice shows any num

Question 1102995: A game is played using 1 dice. If the dice is rolled and shows a 5,
the player wins $5.00. If the dice is rolled and shows a 4, the player
wins $4.00. If the dice shows any number other than 5 or 4, the
player wins nothing.
A: if there is a charge of $1.00 to play the game, what is the game's
expected value?
B: what does this value mean?
C: What are the odds you will win some money playing this game?
Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!
what is the games expected value?

We will subtract the $1 that you play to win, so that
you will win $4 if you roll a 5 and $3 if you roll a
4.

                                 Individual  
Roll   Net win    Probability    Expectation
 1       $0          1/6         $0(1/6)=$0
 2       $0          1/6         $0(1/6)=$0
 3       $0          1/6         $0(1/6)=$0
 4       $3          1/6         $4(1/6)=$3/6
 5       $4          1/6         $5(1/6)=$4/6
 6       $0          1/6         $0(1/6)=$0
 --------------------------------------------
              Total expectation = $(3/6+4/6) = $(7/6) = $1.17
                                          (to nearest penny)

B: what does this value mean?


It means that if you play the game many times, you will lose some 
and win some, but your average winning will be about $1.17 per game.
-----
 C: What are the odds you will win some money playing this game.
There are 6 possible rolls.  On the average out of every 6 you will 
win some money 2 times and win no money 4 times.  So the odds in 
favor of winning some money are 2 to 4, or 2:4, which reduces to
1:2.

Edwin


 

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