1. Consider the gambler's ruin problem. Alice starts with £a; her opponent Bob startswith £(ma). In each round, Alice wins £1 from Bob with probability p, or loses £1to Bob with probability q = 1 - p. Alice ruins if she is reduced to £0; Bob ruins if heis reduced to £0, which means Alice would have £m. Let X denote the amount ofmoney in pounds that Alice has after n rounds. Consider the stochastic process (Xn).pri+1riqri-1 = 0 for i = 1, 2,..., m — 1,rapm - papm-1'Bob gives Alice the opportunity to instead play a different game where the winningsor losses are just 50p per round, still with the same probabilities p and q. For whatvalues of p should Alice prefer to pay this new game?Р

To determine for what values of p Alice should prefer to play the new game where the winnings or…

Answered: Consider the gambler's ruin problem.…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Solve for the following. Write your answer on the space provided. 1. If a card is drawn randomly from a deck of 52 cards, find the probability of getting: a. A jack (j) b. A diamond (d) : c. An ace (A) d. A face card (F) e. A queen (q)
Q7. You go to the shop to buy a toothbrush. The toothbrushes there are red, blue, green, purple and white. The probability that you buy a red toothbrush is Three times the probability that you buy a green one; the probability that you Buy a blue one is twice the probability that you buy a green one; the probabilities of buying green, purple, and white are all equal. You are certain to Buy exactly one toothbrush. For each color, find the probability that you Buy a toothbrush of that color.
Consider a carnival game where a player is given two chances to throw a ball to hit a moving target. Suppose the probability of hitting the target per throw is 0.15. Let X be the number of times the target is hit per game. A. Suppose each game costs $2 dollars to play and a player wins $10 each time the target is hit. So if Y is the amount gained by a player per game, we have the following equation Y=10X-2. Find the expected amount gained by the player per game if this game is repeated many times. B. Find the standard deviation of the amount gained by the player per game if the game is repeated many times.
A person must pay $$8 to play a certain game at the casino. Each player has a probability of 0.15 of winning $$12, for a net gain of $$4 (the net gain is the amount won 12 minus the cost of playing 8).Each player has a probability of 0.85 of losing the game, for a net loss of $$8 (the net loss is simply the cost of playing since nothing else is lost).What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places.
The probability a student has blue eyes is p. Five students are selected at random. Write down, in terms of p, the probability that exactly 3 or exactly 4 of the students have blue eyes. Give your answer in the form 5p3(p- a)(p - b) where a and b are integers.
Suppose you decided to play a gambling game. In order to play the game there is a $1.50 dollar fee to play. If you roll a 1, 2, or 3 you win nothing (i.e., your net profit is $-1.50). If you roll a 4 or 5, you win $3.50 (i.e., your net profit is $2.00). If you roll a 6 you win $5.00 (i.e., your net profit is $3.50).Use the information described above to construct a probability distribution table for the random variable xx which represents the net profit of your winnings. Note: Be sure to enter your probabilities as reduced fractions. Die Roll xx P(x) Roll a 1, 2, or 3 Roll a 4 or 5 Roll a 6 Find the amount you would expect to win or lose each time you played the game. Round your final answer to two decimal places.μ=
A person must pay $$5 to play a certain game at the casino. Each player has a probability of 0.14 of winning $$14, for a net gain of $$9 (the net gain is the amount won 14 minus the cost of playing 5).Each player has a probability of 0.86 of losing the game, for a net loss of $$5 (the net loss is simply the cost of playing since nothing else is lost).What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places.Expected Value = $ If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind? behind ahead
1. Consider each addition problem. Is the sum positive? Select Yes or No for A-C. A. -18 + 27 +(-6) O Yes O No B. 12 + (-19) +5 O Yes O No C. 32+ (-24) + (-6) O No Yes 2. The spinner at right has 8 equal sections, as shown. 1. Choose True or False for each statement. A. The probability of landing on an odd number is . O True O False 6 B. The probability of not landing O True O False 7 on 6 is . 8° C. The probability of landing on a number less than 3 is. O True O False 3 00
Find the probability of getting 6 face cards (king, queen, or jack) when 6 cards are drawn from a deck without replacement. Enter your answer as a fraction. P(6 face cards) =||
A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.56, P(D) = 0.95 and P(B AND D) = 0.39. Find P(D|B). Give your answer as a decimal rounded to the nearest hundredth.
The spinner below is spun twice. If the spinner lands on a border, that spin does not count and spin again. It is equallylikely that the spinner will land in each of the six sectors. For each question below, enter your response as a reduced fraction.Find the probability of spinning blue on the first spin and cyan on the second spin. Find the probability of spinning cyan on the first spin and cyan on the second spin. If the spinner is spun twice, find the probability of spinning red at least once.
using the formula of binomial

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