Taylor is bored so she makes up a game to play. She flips a fair
coin and if lands heads
she records a 1 and if it lands tails she records 2. She continues
to flip the coin till the
sum of the flips is at least 3 and quits playing the game. How many
flips can she expect
before the game is over?
Taylor is bored so she makes up a game to play. She flips a fair coin...
Problem 2: Tails and (Heads or Tails?) Alice and Bob play a coin-tossing game. A fair coin (that is a coin with equal probability of 1. The coin lands 'tails-tails' (that is, a tails is immediately followed by a tails) for the first 2. The coin lands 'tails-heads (that is, a tails is immediately followed by a heads) for the landing heads and tails) is tossed repeatedly until one of the following happens time. In this case Alice wins. first...
Boris and Natasha agree to play the following game. They will flip a (fair) coin 5 times in a row. They will compute S = (number of heads H – number of tails T). a) Boris will pay Natasha S. Graph Natasha’s payoff as a function of S. What is the expected value of S? b) How much should Natasha be willing to pay Boris to play this game? After paying this amount, what is her best case and worst...
8. (Ross, 7.1) A players throws a fair die and simultaneously flips heads, then she wins twice, and if tails, then she wins one-half of the value that appears on the die. Determine her expected winnings a fair coin. If the coin lands
8. (Ross, 7.1) A players throws a fair die and simultaneously flips heads, then she wins twice, and if tails, then she wins one-half of the value that appears on the die. Determine her expected winnings a...
Stacy and George are playing the heads or tails game with a fair coin. The coin is flipped repeatedly until either the fifth heads or the fifth tails appears. If the fifth heads occurs first, Stacy wins the game. Otherwise, George is the winner. Suppose that after the fifth flip, three heads and two tails have occurred. What is the probability that Stacy wins this game?
It’s the same game as before with the same rules: in each round a fair coin is tossed and if it comes up heads you win $1, and if it comes up tails you lose $1. The game consists of 50 such rounds. Your net gain at the end of the game is defined as the total amount of money won by you during the game minus the total amount of money lost by you during the game. Having studied...
Q.1 (25') Pony is playing coin tossing game with Yanny. They found the coin have 4 heads and 6 tails in 10 flips. Let p be the probability for obtaining a head, based on the first 10 flips a) Can we conclude it is a biased or fair coin base on the result above? b) Plot the Bernoulli's PMF What is the probability for obtaining 6 heads in 10 flips using the same coin? d) What is the probability for...
4. Boris and Natasha agree to play the following game. They will flip a coin 5 times in a row. They will compute S = ( number of heads H – number of tails T). a) Boris will pay Natasha S. Graph Natasha’s payoff as a function of S. What is the expected value of S? b) How much should Natasha be willing to pay Boris to play this game? After paying this amount, what is her best case and...
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)?
In a game, a person flips a fair coin twice, and based on the number of heads observed, he will be allowed to shoot so many times (equal to the number of heads observed) on a target. Assume the probability of hitting a target in one shot is 0.2. What is the probability of not hitting the target? Answer [The answer should be a number rounded to five decimal places, don't use symbols such as %]
In a game, a person flips a fair coin twice, and based on the number of heads observed, he will be allowed to shoot so many times (equal to the number of heads observed) on a target. Assume the probability of hitting a target in one shot is 0.2. What is the probability of not hitting the target? [The answer should be a number rounded to five decimal places, don't use symbols such as %]