Game of chance: A player rolls a fair six-sided die. If outcome of a roll is a n

Question

Game of chance: A player rolls a fair six-sided die. If outcome of a roll is a number greater then 4, the player wins 4 dollars. Otherwise, the player looses twice as many dollars as there are dots on the top. Let the random variable X be profit (amount won or lost) per game. a) Make a probability distribution table for the random variable: amount won or lost. b) Find the Expected value of the experiment c) Use Law of Large numbers to interpret the meaning of the Expected value d) If a person plays 100 times, how much he expects to win/loose?

Explanation / Answer

Consider the following table:

a) A probability distribution table for the random variable: amount won or lost is shown below:

b) Consider the following table:

E(X) = xP(x) = -$2.00

c) If this game is played many times, on average person will lost $2.00 per game.

d) For 100 games, expected value is 100(-2.00)=-$200.00

If a person plays 100 times, he expects to loose $200.

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