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A game of chance consists of drawing one card out of ten at random. One card contains the number 100, in which a person, if they chose that card wins $100. A second card contains the number 20, if they chose that card the person wins $20. If any other card is chosen the person losses $16. The game is then played by shuffling cards, facing them down, and having the person choose a card while face down. Once the card is chosen, the outcome is determined, and the card is put back and the deck reshuffled so one can play again.
Please show work as you answer the following questions.
Let the random variable X equal the amount of money won or lost.
x $100 $20 -$16
P(X=x) 0.1 0.1 0.8
a. What is the probability that a person wins three games in a row?
b. Imagine playing this game forever. What does one expect to win or lose per game on average?
c. Calculate s, which is SD(X). Round to two decimal places.
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