SOLUTION: A classmate offers a game for you to play. You roll a single six-sided die, and if the roll is 3 or higher, you win $3. If you roll a 1 or a 2, you owe him $2. Little do you know,

Question 1202738: A classmate offers a game for you to play. You roll a single six-sided die, and if the roll is 3 or higher, you win $3. If you roll a 1 or a 2, you owe him $2. Little do you know, the die is loaded. The probability that you'll roll a 1 is 0.53, and the rest of the values have equal probabilities. What is the expected value of this game?
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.
A classmate offers a game for you to play. You roll a single six-sided die,
and if the roll is 3 or higher, you win $3. If you roll a 1 or a 2, you owe him $2.
Little do you know, the die is loaded. The probability that you'll roll a 1 is 0.53,
and the rest of the values have equal probabilities. What is the expected value of this game?
~~~~~~~~~~~~~~~~~~~~

From the condition, the probability density distribution function is 

    P(1) = 0.53;  P(2) = P(3) = P(4) = P(5) = P(6) =  = 0.094.


Therefore, the expected value of the game is

    -2*P(1) - 2*P(2) + 3*(P(3)+P(4)+P(5)+P(6)) = -2*0.53 - 2*0.094 + 3*4*0.094 = -0.12 dollars.


It means that you will lose 12 cents, in average, in each game, if you play this game many times.

Solved, with complete explanations.

RELATED QUESTIONS
Two fair, normal, six sided dice are used in a game of chance at the bar of the... (answered by Edwin McCravy)

Suppose that you are offered the following "deal." You roll a six sided die. If you roll... (answered by MathLover1)

Cost to play the game is $3.00 You will roll a single die. If you roll a 5 or a 6 you... (answered by ikleyn,Boreal)

You and a friend play a game with a fair, 6-sided die. If you roll a 1 or a 2, you win... (answered by Boreal)

If you flip a fair coin and roll a fair 6-sided die, what are the odds that you flip a... (answered by Boreal)

Roll a die. If you roll a 6 then you win $100, if you do not roll a 6 then you get to... (answered by Positive_EV)

Suppose that you are offered the following "deal." You roll a six sided die. If you roll... (answered by kasperk)

Suppose that you are offered the following "deal." You roll a six sided die. If you roll... (answered by ikleyn)

Could really use some help on a problem, can someone assist? You play a game where a... (answered by lynnlo)