Part 2: Carnival Games At the carnival, you may remember a game where you throw darts to pop two balloons from a wall. The balloons may have prize tokens. For the next player... . There are 50 balloons on the wall and 21 of them each contain a prize token. • The next player pays $2 and gets to throw darts until they pop 2 balloons. Their winnings are based on how many prize tokens they collect. See the table below. Note: The payout of tokens does NOT take into consideration the $2 the player paid. Find the expected value for this game for the next player. Find who the game favors. Complete the tree diagram using non-simplified fractions to label the probabilities. Use T for token and NT for no token. On the right of the tree, list the four outcomes and their final probabilities using non-simplified fractions. Check these add to one. START 1 balloon with a token (T) Use the outcomes' probabilities from the tree to find the expected value of this game. Use all four probabilities in the expected value chart to account for all possibilities. Number of tokens Probability Payout Value = (payout $2 cost) Expected Value for each row 0 $0 2 balloon without a token (NT) $2 $5 Total Expected Value for the player → Does the game favor the player or the game runner?
Part 2: Carnival Games At the carnival, you may remember a game where you throw darts to pop two balloons from a wall. The balloons may have prize tokens. For the next player... . There are 50 balloons on the wall and 21 of them each contain a prize token. • The next player pays $2 and gets to throw darts until they pop 2 balloons. Their winnings are based on how many prize tokens they collect. See the table below. Note: The payout of tokens does NOT take into consideration the $2 the player paid. Find the expected value for this game for the next player. Find who the game favors. Complete the tree diagram using non-simplified fractions to label the probabilities. Use T for token and NT for no token. On the right of the tree, list the four outcomes and their final probabilities using non-simplified fractions. Check these add to one. START 1 balloon with a token (T) Use the outcomes' probabilities from the tree to find the expected value of this game. Use all four probabilities in the expected value chart to account for all possibilities. Number of tokens Probability Payout Value = (payout $2 cost) Expected Value for each row 0 $0 2 balloon without a token (NT) $2 $5 Total Expected Value for the player → Does the game favor the player or the game runner?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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Transcribed Image Text:Part 2: Carnival Games
At the carnival, you may remember a game where you throw darts to pop two
balloons from a wall. The balloons may have prize tokens. For the next player...
• There are 50 balloons on the wall and 21 of them each contain a prize token.
• The next player pays $2 and gets to throw darts until they pop 2 balloons. Their
winnings are based on how many prize tokens they collect. See the table below.
Note: The payout of tokens does NOT take into consideration the $2 the player paid.
Find the expected value for this game for the next player. Find who the game favors.
Complete the tree diagram using non-simplified fractions to label the probabilities.
Use T for token and NT for no token. On the right of the tree, list the four outcomes
and their final probabilities using non-simplified fractions. Check these add to one.
START
1
balloon
with a
token
(T)
Use the outcomes' probabilities from the tree to find the expected value of this game.
Use all four probabilities in the expected value chart to account for all possibilities.
Number of
Expected Value for
tokens
each row
Probability Payout
Value =
(payout - $2 cost)
0
$0
2
balloon
without
a token
(NT)
$2
$5
Total Expected Value for the player →
Does the game favor the player or the game runner?
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