Suppose you play a coin game. There is a 25% chance of making 50%, 50% chance...
Suppose you play a coin game. There is a 25% chance of making 50%, 50% chance of making 10% and 25% of losing 30%. What is the variance of this coin game?
A. 0.35 B. 0.08 C. 0.28 D. 0.13
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Suppose you play a coin game. There is a 25% chance of making
50%, 50% chance...
A boardwalk game of chance costs $1 to play. You have a 25% chance of winning...
A boardwalk game of chance costs $1 to play. You have a 25% chance of winning $1 back, a 20% chance of winning $2 (your $1 back, plus an additional $1), and a 10% chance to win $5 (a gain of $4). What is the expected value of playing the game if you lose your bet 45% of the time?
5. You play a game using an unfair coin. Suppose that each time the coin is...
5. You play a game using an unfair coin. Suppose that each time the coin is tossed, the probability of showing "head" is 1/3 and the probability of showing "tail" is 2/3. Also suppose that each time the coin shows head you win 10 dollars and you lose 3 dollars when it shows tail. How much money do you expect to win when the coin is tossed 10 times?
You play a game of chance that you can either win or lose (there are no...
You play a game of chance that you can either win or lose (there are no other possibilities) until you lose. Your probability of losing is p = 0.54. What is the probability that it a. takes 4 games until you lose. b. takes 7 games until you lose. c. Find the mean c. Find the standard deviation.
(2) Consider the following game of chance. You pay $30 to enter the game. First, you...
(2) Consider the following game of chance. You pay $30 to enter the game. First, you choose a number at random from {1, 2, ..., 20}, and then, independent of this draw, you flip a fair coin 5 times (flips are independent of each other). The host will multiply the number of heads from the 5 flips by the number your draw from {1, 2, ..., 20} and give you that many dollars. (a) What is your expected gain in...
Suppose you can place a bet in the following game. You flip a fair coin (50-50...
Suppose you can place a bet in the following game. You flip a fair coin (50-50 chance it lands heads). If it lands heads, you get 4 dollars, if it lands tails, you pay 1 dollar. This is the only bet you can make. If you don't make the bet you will neither gain nor lose money. What is the utility for you of the coin landing tails if you make the bet (assume utility is dollars)?
Suppose you can place a bet in the following game. You flip a fair coin (50-50...
Suppose you can place a bet in the following game. You flip a fair coin (50-50 chance it lands heads). If it lands heads, you get 4 dollars, if it lands tails, you pay 1 dollar. This is the only bet you can make. If you don't make the bet you will neither gain nor lose money. Should you place the bet?
If you are playing a coin toss game and following is the payoff table Result Payoff...
If you are playing a coin toss game and following is the payoff table Result Payoff Heads Get $25 Tails Lose $25 Assume that you have $100, after you play the game once, how much money will you have? A.$100 since the expected payoff of this game is 0. B. $125 OR $75 C. $625 since the variance of the payoff is 625 D. not enough information
In a certain game of chance, your chances of winning are 0.2 on each play. If...
In a certain game of chance, your chances of winning are 0.2 on each play. If you play the game five times and outcomes of each play are independent, the probability that you win at least once is (A) 0.6723 (B) 0.1091 (C) 0.2000 (D) 0.3277 the answer is A but how is it A
Your probability of winning a game of chance is 0.4. If you play the game 3...
Your probability of winning a game of chance is 0.4. If you play the game 3 times, what is the probability that you will win exactly 2 times?
Suppose that you believe there is a 30% chance that the coin in your hand is...
Suppose that you believe there is a 30% chance that the coin in your hand is biased 80% in favor of heads, and a 70% chance that it’s fair. You flip it twice and get heads both times. What should you now believe is the probability that the coin is fair?
5. You play a game using an unfair coin. Suppose that each time the coin is tossed, the probability of showing "head" is 1/3 and the probability of showing "tail" is 2/3. Also suppose that each time the coin shows head you win 10 dollars and you lose 3 dollars when it shows tail. How much money do you expect to win when the coin is tossed 10 times?
(2) Consider the following game of chance. You pay $30 to enter the game. First, you choose a number at random from {1, 2, ..., 20}, and then, independent of this draw, you flip a fair coin 5 times (flips are independent of each other). The host will multiply the number of heads from the 5 flips by the number your draw from {1, 2, ..., 20} and give you that many dollars. (a) What is your expected gain in...
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