Question

Create your own simple Games Fair game. The game must have a non-uniform probability distribution and 4 or more outcomes. Clearly describe the rules of the game and the points associated with each outcome. Create the points based on an expected value that will allow the game to profit.

Answer 1

We have a box containing 4 different type colour of balls green ,blue ,white and black there are total 20 balls in the box the number of diffetedicolour balls are given below

◆green - only 1 ball

◆blue - 4 balls

◆white - 8 balls

◆black - 7 balls

If you want to get a chance to select a ball from the box you must pay $2 and it will not get back if you win or loss

Each ball colour wins different type of amount.

The amount that are given to the player if he select

●green =$20

●blue =$3

●white =$1

●black =$0

Would you play the game.......

Probability of getting green ball=1/20

Probability of getting blue ball =4/20

Probability of getting white ball =8/20

Probability of getting black ball =7/20

Change that comes in to our amount after selecting a ball is given if

Select a green ball = $20-$2= $18

Select a blue ball = $3-$2 =$1

Select a white ball =$1-$2 = -$1

Select a black ball =$0-$2= -$2

Hence

Expected value = (1/20*18)+(4/20*1)+(8/20*-1)+(7/20* -2)

=(18/20)+(4/20)+( -8/20)+( -14/20)

=(18+4 -8 -14)/20

=(22 -22)/20 =0/20

=0

We got the expected value 0 says that the game is a fair game .

Here we got expected value exactly 0 means neither profit nor loss if we are looking forward for the profit we should get an expected value more than 0 . If we get an expected value 0.05 means we have a profit of 0.05 on each try.