Math  /  Data & Statistics

Question51
Select ALL the correct answers.
Which of the following situations are fair? To decide which citizens will be asked to participate in a county-wide poll, each citizen is assigned a number and the county uses a random number generator to determine the citizens who will be contacted. Jason plays a game in which he has to pick a ball from a box of 10 balls, which contains 7 black balls and 3 white balls. He wins the game if he draws a white ball in one attempt. Jericho designs a game for a school carnival. The game consists of a box of 50 colored balls; 35 are violet, 10 are orange, and 5 are yellow. The player has to choose one ball from the box. The player wins $5\$ 5 if it is a yellow ball, otherwise, the player wins nothing.
Ryan designs a game where a prize wheel is split into five equal sections. Four sections are red and one is green. If the wheel is spun and lands on a red section, the players loses $1\$ 1. If the wheel lands on green section, the player wins $5\$ 5.
Ray is playing a game in which he rolls a six-sided number cube. If the outcome is six, he is paid $5\$ 5. Otherwise, he loses \$1.
Jack and Mia both want the last cookie and neither will agree to share by splitting it. They ask a stranger passing by to flip a coin to decide who gets the cookie. (c) 2024 Edmentum. All rights reserved.

Studdy Solution

STEP 1

1. A fair situation is one where each participant has an equal chance of winning or being selected.
2. The fairness of a game or selection process is determined by the probability of each outcome.

STEP 2

1. Analyze the fairness of the county-wide poll selection.
2. Analyze the fairness of Jason's game.
3. Analyze the fairness of Jericho's carnival game.
4. Analyze the fairness of Ryan's prize wheel game.
5. Analyze the fairness of Ray's number cube game.
6. Analyze the fairness of Jack and Mia's coin flip.

STEP 3

In the county-wide poll, each citizen is assigned a number, and a random number generator is used to select participants. This method gives each citizen an equal chance of being selected, making it fair.

STEP 4

Jason's game involves picking one ball from a box with 10 balls (7 black, 3 white). The probability of winning (drawing a white ball) is 310\frac{3}{10}. Since the chances are not equal for each ball color, this situation is not fair.

STEP 5

Jericho's game involves picking one ball from a box with 50 balls (35 violet, 10 orange, 5 yellow). The probability of winning (drawing a yellow ball) is 550=110\frac{5}{50} = \frac{1}{10}. The chances are not equal for each ball color, making this situation not fair.

STEP 6

Ryan's prize wheel has five equal sections (4 red, 1 green). The probability of winning (landing on green) is 15\frac{1}{5}, while the probability of losing (landing on red) is 45\frac{4}{5}. Since the probabilities are not equal, this situation is not fair.

STEP 7

Ray's game involves rolling a six-sided number cube. The probability of winning (rolling a six) is 16\frac{1}{6}, while the probability of losing is 56\frac{5}{6}. Since the probabilities are not equal, this situation is not fair.

STEP 8

Jack and Mia's coin flip involves a fair coin, giving each a 12\frac{1}{2} chance of winning. This situation is fair because both have an equal probability of winning.
The fair situations are: - The county-wide poll selection. - Jack and Mia's coin flip.

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