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Assume that two players, Renée and Carlos, play a game with the following payoff matrix (to Renée):
a. Is the game strictly determined? Determine the strategy for each player.
b. What is the value of the game? Is the game fair?
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Chapter 9 Solutions
Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
- In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game. = Win a prize = Do not win a prize 1. Start by determining the probabilities for winning a prize and not winning a prize. Draw a probability tree to find the possible outcomes and the probabilities. After you draw the tree, check you work by clicking on the link below. Click to hide hint CHIP 1 CHIP 2 Probability P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25 0.5 0.5 0.5 P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25 Start 0.5 0.5 P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25 0.5 P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25arrow_forwardConsider the game described by the following table. What is the best response for the column player if s/he knows that the row player will make the Y move? B OA O C ROW PLAYER O There is no definitive answer. X Y COLUMN PLAYER A 4, -1 3, -1 B -1,0 -2,4 C 2,1 0,2arrow_forwardConsider the following normal form of a game. A B C OC OA OD OB (-3,-4) (-1,0) What is the maximin strategy of the row player? D (-2,-5) (-4,-3)arrow_forward
- In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game.arrow_forwardA 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.arrow_forwardIf a = (-6, 12, -9), b = (2, -16, 18), and c = (28, -14, 3), what is 3. 6+2c? 2 %3D %3D (51, 0, -24) (57, -48, 30) (24, -18, 12) (20, 14, -24) C.arrow_forward
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- California Lotto officials want to try out a new "big wheel" game. This new game actually consists of two big wheels (spinners). The contestants spin Spinner 1, and then immediately after, they spin Spinner 2 to determine the "multiplier." When both spinners have stopped turning, the dollar amount shown on Spinner 1 is multiplied by the "multiplier" on Spinner 2 and the contestant wins that much money. $100800 20 50 150dp $1000 0.5 135° s5000 100 Spinner 1 Dollars Spinner 2 Multipliers What is the probability of winning the largest amount of money?arrow_forwardNigel and Sofia play the following game. Each of them roll a fair six-sided die once. IfSofia’s number is greater than or equal to Nigel’s number, she wins the game. But ifSofia rolled a number smaller than Nigel’s number, then Nigel rolls again. If Nigel’ssecond roll gives a number that is less than or equal to Sofia’s number, the game endswith a draw. If Nigel’s second roll gives a number larger than Sofia’s number, Nigelwins the game.Find the probability that Nigel wins the game and the probability that Sofia wins thegame.arrow_forwardOne option in a roulette game is to bet $7 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $7 you paid to play the game and you are awarded $7. If the ball lands elsewhere, you are awarded nothing and the $7 that you bet is collected. Complete parts (a) through (b) below. III a. What is the expected value for playing roulette if you bet $7 on red? $ (Round to the nearest cent.) b. What does this expected value mean? Choose the correct statement below. O A. This value represents the expected loss over the long run for each game played. OB. Over the long run, the player can exper to break even. OC. This value represents the expected win over the long run for each game played.arrow_forward
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