Homework Answers
| P(x) | x | x*P(x) | |
| A | 0.364 | 8.000 | 2.909 |
| B | 0.273 | 0.000 | 0.000 |
| C | 0.273 | 0.000 | 0.000 |
| D | 0.091 | 0.100 | 0.009 |
| 1.000 | 2.918 |
Expected winnign is 2.918 is the answer
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(1 point) Consider the following game of chance based on the spinner below: Each spin costs...
(1 point) Consider the following game of chance based on the spinner below: Each spin costs...
(1 point) Consider the following game of chance based on the spinner below: Each spin costs $4. If the spinner lands on D the player wins $9, if the spinner stops on B the player wins a penny otherwise the player wins nothing. Calculate the players expected winnings. Express your answer to at least three decimal places in dollar form. Answer: $ 3/10 1/5 1/18 2/5
Consider the following game: We spin the spinner. If the outcome is favorable for E, then...
Consider the following game: We spin the spinner. If the outcome is favorable for E, then we win 1 unit. If the outcome is not favorable for E, then we neither win nor lose anything. Compute the expected value, E.V., for this game and compare it to P(E), which is 60%. You should discover a coincidence that holds for this kind of game, but which is not true for every game.
Problem 1: Game Spinner We will be comparing empirical (relative frequencies based on an observation of...
Problem 1: Game Spinner We will be comparing empirical (relative frequencies based on an observation of a real-life process) to theoretical (long-run relative frequency) probabilities. We will use StatCrunch to simulate this process using a board game spinner three times so that we can determine the total number of spaces moved in three turns. The board game spinner looks like the image below. The spinner is equally likely to land on any given section. f) Calculate the theoretical probability of...
Consider the following game. You choose a color on the spinning wheel to the right and...
Consider the following game. You choose a color on the spinning wheel to the right and pay a price of $3 to spin the wheel. If your color comes up, you get $3 back plus $3 additionally. Otherwise, you get nothing. a. What is the expected financial outcome from this game (in dollar amount)? nothing dollars. (Round up to 2 digits after the decimal point.) b. What price of the game would ensure that the expected financial outcome is positive?...
4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the...
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Consider a play of the casino game `Quick Draw'. In this game, a player pays $11...
Consider a play of the casino game `Quick Draw'. In this game, a player pays $11 to play. The player picks one card from a standard pack of 52 cards (i.e. there are four A’s and four K’s in a standard pack of 52 cards). If the player gets an Ace, they win $50 but loose the amount they paid to play (the profit is revenue minus cost); if the player selects a King, they win $30 but loose the...
(1 point) A game of chance involves rolling an unevenly balanced 4-sided die. The probability that...
(1 point) A game of chance involves rolling an unevenly balanced 4-sided die. The probability that a roll comes up 1 is 0.21, the probability that a roll comes up 1 or 2 is 0.44, and the probability that a roll comes up 2 or 3 is 0.55 . If you win the amount that appears on the die, what is your expected winnings? (Note that the die has 4 sides.)
A game of chance offers the following odds and payoffs. Each play of the game costs...
A game of chance offers the following odds and payoffs. Each play of the game costs $200, so the net profit per play is the payoff less $200. Probability 0.30 0.60 0.10 Payoff $600 200 Net Profit $400 0 -200 a-1. What is the expected cash payoff? (Round your answer to the nearest whole dollar amount.) a-2. What is the expected rate of return? (Enter your answer as a percent rounded to the nearest whole number.) b-1. What is the...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players pl...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players play smartly (nobody plays a fool move trying to let the opponent wins. But there is only one winner anyway) a)If the person getting the last stick wins, will the first player win? Why? Show the steps the first and second player will...
. (15 pts) Consider milti- r a multi-player zame over the Internet where N players attempt to shoot a monster rrain) in a random fashion as controlled by a game server. The agent program at each...
. (15 pts) Consider milti- r a multi-player zame over the Internet where N players attempt to shoot a monster rrain) in a random fashion as controlled by a game server. The agent program at each player site maintains a variable that indlicates who shot the monster. The variable at ith player site, denoted as tes," is set to j if lhe İth player believes that jth player shot the monster. Here, the display at player i shows a scoreboard...
(1 point) Consider the following game of chance based on the spinner below: Each spin costs $4. If the spinner lands on D the player wins $9, if the spinner stops on B the player wins a penny otherwise the player wins nothing. Calculate the players expected winnings. Express your answer to at least three decimal places in dollar form. Answer: $ 3/10 1/5 1/18 2/5
Problem 1: Game Spinner We will be comparing empirical (relative frequencies based on an observation of a real-life process) to theoretical (long-run relative frequency) probabilities. We will use StatCrunch to simulate this process using a board game spinner three times so that we can determine the total number of spaces moved in three turns. The board game spinner looks like the image below. The spinner is equally likely to land on any given section. f) Calculate the theoretical probability of...
4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the player pays $10 to play. He/she picks onē card from the standard deck of 52 cards (i.e. four A's, four K's, etc.). If the player selects an "A", he/she wins $50 (i.e. the profit is $40); if the player selects a "K", he/she wins $30 (i.e. the profit is $20). Otherwise, the player wins nothing and also loses the bet of $10. Let the...
A game of chance offers the following odds and payoffs. Each play of the game costs $200, so the net profit per play is the payoff less $200. Probability 0.30 0.60 0.10 Payoff $600 200 Net Profit $400 0 -200 a-1. What is the expected cash payoff? (Round your answer to the nearest whole dollar amount.) a-2. What is the expected rate of return? (Enter your answer as a percent rounded to the nearest whole number.) b-1. What is the...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players play smartly (nobody plays a fool move trying to let the opponent wins. But there is only one winner anyway) a)If the person getting the last stick wins, will the first player win? Why? Show the steps the first and second player will...
. (15 pts) Consider milti- r a multi-player zame over the Internet where N players attempt to shoot a monster rrain) in a random fashion as controlled by a game server. The agent program at each player site maintains a variable that indlicates who shot the monster. The variable at ith player site, denoted as tes," is set to j if lhe İth player believes that jth player shot the monster. Here, the display at player i shows a scoreboard...
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