Game of chance: A player rolls a fair six-sided die. If outcome of a roll is a n
ID: 3233792 • Letter: G
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.
Outcome Win/Loss, x 5 or 6 4 1 -2 2 -4 3 -6 4 -8Related Questions
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