1. Find solutions, where possible, for the cube game pictured below. R Cube 1 w|R|GB G Cube 3 w|RwB G R Cube 2 BBGW В Cube 4
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- A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not 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. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $ (c) Is this game fair? Yes NoAt 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 a 3 and the coin shows tails, then you win $22. If the coin shows heads and the die shows an even number, then you win $9. Otherwise, you do not 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. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent.
- A certain game involves tossing 3 fair coins, and it pays 17c for 3 heads, 8 for 2 heads, and 2c for 1 head. Is a fair price to pay to play this game? That is, 8c does the cost to play make the game fair?Ashleigh and Pavak play a game that begins with a pile of 100 toothpicks. They alternate turns with Ashleigh going first. On each player’s turn, they must remove 1, 3, or 4 toothpicks from the pile. The player who removes the last toothpick wins the game. Determine, with proof, which player has a winning strategy.If I $6 to play a spinner game and the chances of winning $1 dollar is 50% and the chances of winning $12 is 50%. What is the fair price of the game?
- Jane draws a marble from a box containing 5 red marbles, 3 green marbles, and4 blue marbles. She receives $2 for a red marble and $3 for a green marble that she draws.If she draws a blue marble, she loses $4. Is the game fair? How many dollars should Janepay for a draw in a fair game?18. Michael playsa game where he wins $5 if he draws an ace from a deck and loses $0.50 for all other cards he draws. What payout would make this a fair game?A game involves drawing a single card from a standard deck. The player receives $10 for an ace, $5 for a king, and $1 for a red card that is neither an ace nor a king. Otherwise, the player receives nothing. If the cost of each draw is $2, should you play? Explain your answer mathematically.
