From the given information, the following is the probabilty distribution
outcomes | 0 head | 1 head | 2 heads |
winning amount(x) | 1 | 2 | 5 |
p (x) | 0.25 | 0.5 | 0.25 |
i) Expected winnings = X * P(X) = 1 * 0.25 + 2 * 0.5 + 5 * 0.25 = 2.5
ii) For fair Game, Expected value = 0
i.e So if it is fair game he has pay $2.5, since it the expected return which is reversed amount
A player tosses two fair coins. He wins $5 if 2 heads occur, $2 it 1...
A player pays $4 to play the following game: He tosses three fair coins and receives back “payoff” of $1 if he tosses no heads, $2 for one head, $4 for 2 heads, and $6 for 3 heads.Find the player’s expected net winnings for this game.
In a game called heads, a player tosses a coin three times. S/he wins N$300 if 3 heads occur, N$200 if 2 heads occur, and N$100 if 1 head occurs. On the other hand, S/he loses N$1500 if no head occurs. Let Y be a random variable denoting the player's gain (or loss). The coin is biased such that the probability of landing heads up is 2/3. a) Find the probability distribution of Y b) Hence, or otherwise, find the...
A game is played in which two quarters are tossed. If two heads come up, the player wins $1. If a head and a tail come up, the player wins $0.50. If two tails come up, the player wins$0.25. If the game is to be fair, how much should a player expect to pay to play the game?
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3. Weston is playing a game where on each turn, he flips two fair coins. If both are heads, then he wins. Otherwise, he continues playing. If he wins the game on the third turn, what is the expected number of heads flipped throughout this process, including those from the winning turn?
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2. A game of chance costs $5 to play and consists of rolling a five fair dice. If at least four of the dice shows a number (strictly) greater than 2 then the player wins $10. (a) What is the expected net winnings from one game? (b) Suppose that a gambler plans to keep playing this game until he has lost a total of four games, what is his expected net loss or net winnings under this strategy?
2. A player pays $3 to play the following game: He rolls a die and receives $7 if he tosses a 6 and $1 for anything else. Find the player's expected net winnings for the game. What is the standard deviation?
If a gambler rolls two dice and gets a sum of seven, he wins $10, and if he gets a sum of four, he wins $25. The cost to play the game is $5 A.Give the probability distribution of the winnings for this game. B. What are the expected winnings for a person who plays this game?
A subtraction game Subtraction games are two-player games in which there is a pile of objects, say coins. There are two players, Alice and Bob, who alternate turns subtracting 4.9. A SUBTRACTION GAME 19 from the pile some number of coins belonging to a set S (the subtraction set). Alice goes first. The first player who is unable to make a legal move loses. For example, suppose the initial pile contains 5 coins, and each player can, on his turn,...