end of semester test\n12\nselect all the correct answers.\nwhich of the following situations are fair?\nto…

end of semester test\n12\nselect all the correct answers.\nwhich of the following situations are fair?\nto 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.\njericho 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 if it is a yellow ball, otherwise, the player wins nothing.\nryan 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. if the wheel lands on green section, the player wins $5.\njason 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.\njack 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.\nray is playing a game in which he rolls a six - sided number cube. if the outcome is six, he is paid $5. otherwise, he loses $1.

end of semester test\n12\nselect all the correct answers.\nwhich of the following situations are fair?\nto 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.\njericho 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 if it is a yellow ball, otherwise, the player wins nothing.\nryan 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. if the wheel lands on green section, the player wins $5.\njason 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.\njack 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.\nray is playing a game in which he rolls a six - sided number cube. if the outcome is six, he is paid $5. otherwise, he loses $1.

Answer

Explanation:

Step1: Analyze the county - wide poll situation

Random number generator gives equal probability to each citizen, so it is fair.

Step2: Analyze Jericho's game

Probability of getting a yellow ball is $\frac{5}{50}=\frac{1}{10}$. The pay - off structure may not be balanced with the probability, so it may not be fair.

Step3: Analyze Ryan's game

Probability of landing on red is $\frac{4}{5}$ and on green is $\frac{1}{5}$. Expected value: $E = \frac{4}{5}\times(- 1)+\frac{1}{5}\times5=\frac{-4 + 5}{5}=\frac{1}{5}>0$, not a fair - game in a strict sense as the expected value is non - zero.

Step4: Analyze Jason's game

Probability of drawing a white ball is $\frac{3}{10}$, no information about pay - offs to determine fairness.

Step5: Analyze Jack and Mia's situation

Coin flip has two equally likely outcomes (heads or tails), so it is fair.

Step6: Analyze Ray's game

Probability of getting a six is $\frac{1}{6}$, and probability of not getting a six is $\frac{5}{6}$. Expected value: $E=\frac{1}{6}\times5+\frac{5}{6}\times(-1)=\frac{5 - 5}{6}=0$, so it is fair.

Answer:

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. 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. Ray is playing a game in which he rolls a six - sided number cube. If the outcome is six, he is paid $5. Otherwise, he loses $1.