Consider the following game: A nickel is taken from a jar. Player A tosses the nickel. Then Player B tosses the same nickel. If Player B’s toss matches Player A’s toss then B wins the nickel. If the tosses are different, then A wins the nickel. Who is more likely to win this game, and why? Think about this problem realistically: you don’t know anything about the coin except that it appears

Consider the following game: A nickel is taken from a jar. Player A tosses the nickel. Then Player B tosses the same nickel. If Player B’s toss matches Player A’s toss then B wins the nickel. If the tosses are different, then A wins the nickel. Who is more likely to win this game, and why? Think about this problem realistically: you don’t know anything about the coin except that it appears

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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A. Marble Game John has designed a marble game. 1. Bag A contains 3 marbles – one red, one blue and one green. Bag A Bag B Bag B contains 2 marbles - one red and one blue. To play this game, a player draws one marble from each bag without looking. If the two marbles match (are of the same color), the player wins a prize. What is the probability of winning a prize at a single try? R B B Show your work.
2. Janelle plays a game in which she chooses a card at random from a standard deck of 52 cards. If the card selected is a face card, she wins $2; if it is an ace, she wins $5; if it is an even numbered card, she wins $1; but if it is an odd numbered card, she loses $3. Find her expected gain for this game.
Consider a repeated game in which the following stage game is repeated 2 times. Total payoff = undiscounted sum of payoffs from all stages. Player 1 U M D L 7,3 7,7 15,7 Player 2 C 11,7 7,9 7, 11 R 3,5 1, 11 5,9 The lowest total payoff that player 1 can get in this repeated game is:
Consider the following game played with an ordinary deck of 52 playing cards: Thecards are shuffled and then turned over one at a time. At any time, the player canguess that the next card to be turned over will be the ace of spades; if it is, then theplayer wins. In addition, the player is said to win if the ace of spades has not yetappeared when only one card remains and no guess has yet been made. What is a goodstrategy? What is a bad strategy?
In craps which of the following scenarios is least likely? (Remember, for each roll you're rolling two dice, so rolling a 7" means any combination of dice that adds to 7.) A. Roll an 8 on the first roll, and an 8 on the second roll to win the game. B. Roll a 4 on the first roll, and a 7 on the second roll to lose the game. C. Roll a 7 on the first roll to win the game. D. Roll a 6 on the first roll, and a 6 on the second roll to win the game. O E. Roll a 2, 3, or 12 on the first roll to lose the game.
10. Rachel is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rachel tosses the dart once. She wins $1 if the dart lands in slice 1, $2 if the dart lands in slice 2, $5 if the dart lands in slice 3 , and $8 if the dart lands in slice 4. She loses $2.50 if the dart lands in slices 5, 6, 7, or 8. (a) Find the expected value of playing the game. dollars (b) What can Rachel expect in the long run, after playing the game many times? Rachel can expect to gain money. She can expect to win ( ) dollars per toss. Rachel can expect to lose money. She can expect to lose ( ) dollars per toss. Rachel can expect to break even (neither gain nor lose money).
More random outcomes For each of the following scenarios, decide if the outcome is random. a) You enter a contest in which the winning ticket is selected from a large drum of entries. Was the winner of the contest random? b) When playing a board game, the number of spaces you move is decided by rolling a six-sided die. Is the number of spaces you move random? c) Before flipping a coin, your friend asks you to “call it." Is your choice (heads or tails) random?
A. P (win/regular) = 0.82 P (win/prevent) = 0.64 Conclusion: You are more likely to win by playing prevent defense. B. P (win/regular) = 0.33 P (win/prevent) = 0.67 Conclusion: You are more likely to win by playing prevent defense. C. P (win/regular) = 0.82 P (win/prevent) = 0.64 Conclusion: You are more likely to win by playing regular defense. D. P (win/regular) = 0.33 P (win/prevent) = 0.67 Conclusion: You are more likely to win by playing regular defense.
The St. Petersburg paradox is a coin flip game, where a fair coin is tossed successively, until heads occurs. If the first toss is heads, you win $1. If the first one is tails and the second one is heads, you win $2. If the first heads occurs in the third toss, you win $4 and so forth. The amount of money you win is doubled with each coin flip you survive. In the eighteenth century it was believed that the fair price for participating in such a game would be the expected wealth you gain. Show that the expectation value of the St. Petersburg game is infinite.
When playing games of chance like roulette, people often say that a particular outcome is due, implying that one income is more likely because it has not happened in a while. This is fallacy because in these examples of outcome of each trial is: a. independent b. dependent c. subjective d. interrelative
On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this process
A player pays 4 to play the following game The player tosses three fair coins and receives payoifs of 1 if he tosses no heads, 2 for one head, 3 for two heads, and 5 for three heads. What is the player's expected net winnings (or loss) for the game?