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A game costs $3.00 to play. A player can win $1.00, $5.00, $10.00, or nothing at...

A game costs $3.00 to play. A player can win $1.00, $5.00, $10.00, or nothing at all. The probability of winning $1.00 is 40%, $5.00 is 20%, and $10.00 is 5%.

a) What is the probability of winning nothing at all?

b) Calculate the expected value for this game.

c) Explain whether this game is fair.  

Math   Statistics-And-Probability   
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Answer #1

Here' the answer with all formulae. Write back in case you've doubts.

a. P(nothing at all) = 1-P(winning $1, $5, $10)
= 1-(.4+.2+.05)
= .35

b. Expected value of this game is the probability weight return of each scenario - cost to play the game
= $(.35*0 + .4*1* + .2*5 + .05*10 - 3)
= -$2.1

c. The game is NOT fair on the player. If it were fair then expected value of playing the game would have been $0. Its negative 2.1 or -$2.1 , indicating he will make a "loss" on average

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