At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1-4), noting the number showing. If the die shows 3 and the coin shows tails, then you win $21. If the coin shows heads and the die shows an even number you win $12. Otherwise you don't win anything. Let X be your net winnings. a. Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. X P(X) b. Compute your expected net winnings for the game. Round your answer to the nearest cent, c. Is this game fair? ? v

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side
showing, and roll a fair standard 4-sided die (numbered 1-4), noting the number showing.
If the die shows 3 and the coin shows tails, then you win $21. If the coin shows heads and the die shows an even number you win $12. Otherwise you don't win
anything.
Let X be your net winnings.
a. Create a probability distribution for X. Enter the possible values of X in ascending order from left to right.
P(X)
b. Compute your expected net winnings for the game. Round your answer to the nearest cent,
2$
c. Is this
game
fair? ?
Transcribed Image Text:At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1-4), noting the number showing. If the die shows 3 and the coin shows tails, then you win $21. If the coin shows heads and the die shows an even number you win $12. Otherwise you don't win anything. Let X be your net winnings. a. Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. P(X) b. Compute your expected net winnings for the game. Round your answer to the nearest cent, 2$ c. Is this game fair? ?
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