Question

Scenario: There is a box containing 4 different type color of balls green, blue, white and black there are total 20 balls in the box the number of different colored 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 color wins different type of amount. The amount that are given to the player if he selects

green =$20 blue =$3 white =$1 black =$0

Would you play the game if; 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 into 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 is: = (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 an expected value of 0, meaning 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, this means we have a profit of 0.05 on each try.

QUESTION= What is the THEORETICAL RESULTS and how does your experimental probability distribution results compare to them. Were they close? If they weren't close, what are some possible reasons why?

Answer 1

Solution: