Question

In: Statistics and Probability

Problem 5 (6 pts). A and B play a series of games. Each game is independently...

Problem 5 (6 pts). A and B play a series of games. Each game is independently won by A with probability p and by B with probability 1 − p. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the grater number of total wins is declared the winner of the series. Find the probability that a total of 4 games are played.

Solutions

Expert Solution


Related Solutions

Two team (A and B) play a series of baseball games. The team who wins three...
Two team (A and B) play a series of baseball games. The team who wins three games of five-game-series wins the series. Consider A has home-field advantage (0.7 means A has probability of winning 0.7 if it plays in its field) and opponent-field disadvantage (0.2 means A has probability of winning 0.2 if it plays in opponents field). If the series start on A team’s field and played alternately between A and B team’s fields, find the probability that series...
1) Two teams, A and B, are playing a best of 5 game series. (The series...
1) Two teams, A and B, are playing a best of 5 game series. (The series is over once one team wins 3 games). The probability of A winning any given game is 0.6. Draw the tree diagram for all possible outcomes of the series. 2) List all possible combinations of rolling a 4-sided die (d4) and a 6-sided die (d6) (enumaration). Also determine the probability X {1..6} where X is the largest of the two numbers. Two players, A...
5. Consider the following games played between two players, A and B.   Game 1: A and...
5. Consider the following games played between two players, A and B.   Game 1: A and B have reached a verbal agreement: A would deliver a case of beer to B, and B would deliver a bag of beer nuts to A. Now, each player needs to take an action: keep the promise (to deliver the goods), break the promise. If both keep their promises, then each player gets a payoff of 5; if both break their promises, then each...
Two players A and B play a dice game with a 6-face fair dice. Player A...
Two players A and B play a dice game with a 6-face fair dice. Player A is only allowed to roll the dice once. Player B is allowed to roll the dice maximally twice (that is, Player B can decide whether or not she or he would roll the dice again after seeing the value of the first roll). If the player with the larger final value of the dice wins, what is the maximal probability for Player B to...
Problem 2. You pay 5$ /round (nonrefundable) to play the game of rolling a pair of...
Problem 2. You pay 5$ /round (nonrefundable) to play the game of rolling a pair of fair dice. If you roll an even sum, you lose, no pay off. If you roll an odd sum, that's your win (say, roll of 7 pays you 7$). Discrete random variable X represents the winnings. For example, the lowest value of X is x=0 when you roll an even sum. For example, x=3 only when you roll {1,2} or {2,1}. You win 1+2=3$...
Problem 2. You pay 5$ /round (nonrefundable) to play the game of rolling a pair of...
Problem 2. You pay 5$ /round (nonrefundable) to play the game of rolling a pair of fair dice. If you roll an even sum, you lose, no pay off. If you roll an odd sum, that's your win (say, roll of 7 pays you 7$). Discrete random variable X represents the winnings. For example, the lowest value of X is x=0 when you roll an even sum. For example, x=3 only when you roll {1,2} or {2,1}. You win 1+2=3$...
You are to play three games. In the first game, you draw a card, and you...
You are to play three games. In the first game, you draw a card, and you win if the card is a heart. In the second game, you toss two coins, and you win if one head and one tail are shown. In the third game, two dice are rolled and you win if the sum of the dice is 7 or 11. What is the probability that you win all three games? What is the probability that you win...
A particular baseball team wins 68% of its games. Next week it will play 6 games....
A particular baseball team wins 68% of its games. Next week it will play 6 games. (a) What is the team’s expected number of wins during that week? (Round your answer to 2 decimal places.) (b) What is the probability that the team will win at least 5 games next week?
Problem 12. Peter and Paula play a game of chance that consists of several rounds. Each...
Problem 12. Peter and Paula play a game of chance that consists of several rounds. Each individual round is won, with equal probabilities, by either Peter or Paula; the winner then receives one point. Successive rounds are independent. Each has staked 50 for a total of 100, and they agree that the game ends as soon as one of them has won a total of 5 points; this player then receives the 100. After they have completed four rounds, of...
Question 6: Winston, a dog, loves to play fetch. He catches each ball mid-air independently with...
Question 6: Winston, a dog, loves to play fetch. He catches each ball mid-air independently with probability 0.4. Write a simulation in R in which you throw Winston five balls and compute how many of the five balls he catches mid-air. Repeat this simulation N=5,000 times. a) Plot a histogram of the number of catches Winston has made in each series of five catches. b) What proportion of the time does Winston catch exactly two balls mid-air? c) What proportion...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT