Suppose a family consisting of a father and a son plays a"Gambler's ruin" game for the Chinese New Year Eve. Each game consists ofa sequence of plays. It starts with both son and father having 2 tokens, andone token is bet at each play. The game ends when either the son or the fathercollects all 4 tokens. At each play the probability for the father to win thetoken is 1-p. What should be the value of p in order for the father to enjoythe "house advantage" of 10% ?

Let:q be the probability of the father winning a token.p be the probability of the son winning a…

Answered: Suppose a family consisting of a father…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Your friend offers to place a bet with you. He will pay you $2 if your favorite sports team wins the game on Tuesday night. But you will pay him $3 if his team wins. Your team has an 55% chance of winning, whereas his only has a 45% chance. This bet is in your favor. True or False?
Your probability professor has a tabby cat who sleeps 34% of the time and seems to respond to stimuli more or less randomly. If a human pets her when she’s awake, she will request more petting 8% of the time, food 38% of the time, and a game of fetch the rest of the time. If a human pets her when she’s asleep, she will request more petting 33% of the time, food 41% of the time, and a game of fetch the rest of the time. (You can assume that the humans don’t pet her disproportionally often when she’s awake.) • If the cat requests food when petted, what is the probability that she was asleep? • If the cat requests a game of fetch when petted, what is the probability that she was not asleep?
a pair of dice is rolled once. Suppose that you lose 9$ if the dice sum to 5 and win 10$ if the dice sum to 11 or 8. How much should you win or lose if any other number turns up in order for the game to be fair?
snip
A and B play the following game. They throw alternatively a pair of dice. Whosoever gets sum of the two numbers on the top as seven wins the game and the game stops. Suppose A starts the game. Find the probability (a) A wins the game (b) B wins the game.
Please help!!! Q4. Ariana and Bella are playing a game. They each have 4 cards, which are numbered 1, 2, 3 and 4. Each shuffles her own cards and turns one over at random. If the cards show the same number, Ariana wins and Bella must pay Ariana $3. If the cards show different numbers, Bella wins and Ariana must pay Bella $1. By finding the probabilities of Ariana and Bella winning, show whether or not the game is fair.
A coffee shop has a "manager surprise" drink that randomly chooses among 4 drinks. If Lee goes to the coffee shop for 3 days, what are the odds Lee would have been given the same drink all 3 days?
A prize is placed at random in one of three boxes. You pick a box (and do not open it). Now, the dealer (who knows where the prize is) chooses one of the other two boxes, opens it and shows you that it is empty. She then gives you the opportunity to keep your original box or switch to the other unopened box. Find the probability of winning the prize if you switch. Find the probability of winning the prize if you stay. Should you stay or switch?
A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try? Kay has an 80% probability of making a free-throw in basketball, and each free-throw is independent. Kay gets to take 2 free-throws and must make both to win the game. What is the probability that Kay's team will win the game? Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo’s margin of error, rounded to the nearest whole number? (The formula is )
A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot? 1/30 = 0.03 or 3% 3/(30+30+30) = 3/90 = 0.33 or 33% 3/(30×30×30) = 3/27000 = 0.0001 or 0.01% 1/(30×30×30) = 1/27000 = 0.00003 or 0.003% Question 18
Three students ABC are in a running race. A and B have the same probability of winning and each is twice as likely to win as C. Find the probability that B or C wins.

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