Question

An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball, and a player is to draw one ball. If it is black, he wins $1, if it is red, he wins $2, if it is white he wins $3 and if it is blue, he pay $25.

a. Set up the empirical probability distribution for the random variable X, the payoff of the game.

Game Payoff (X)	Probability [P(X)
$1
$2
$3
$4

b. What is the mathematical expectation of this game?



c. In the long-run, will the player win or lose?

Answer 1

Solution:

In the question, we are given:

An urn contains 7 black balls, 4 red balls, 3 white balls, and 1 blue ball, and a player is to draw one ball. If it is black, he wins $1, if it is red, he wins $2, if it is white he wins $3 and if it is blue, he pays $25.

Therefore, there are total 7+4+3+1=15 balls.

The probability of drawing a black ball is:

The probability of drawing a red ball is:

The probability of drawing a white ball is:

The probability of drawing a blue ball is:

Game Payoff (X)	Probability P(X)
$1	0.46667
$2	0.26667
$3	0.2
-25	0.06667

b. What is the mathematical expectation of this game?

  

  


c. In the long-run, will the player win or lose?

Answer: In the long-run, the player will lose.