Explanation Calculation: Define the random variable Y as gambler wins exactly once before gambler loses initial capital. Let event W represents that gambler wins the game with probability P ( W ) = 0.10 and event L represents that gambler loses the game with probability P ( L ) = 0.90 It costs $10 for playing the game and $80 can be won if gambler wins the games. The gambler commences with amount $30. The first possibility that Y can take is WLLLLLLLLLL , because for playing the first game gambler spends $10, then gambler has $20 ( $ 30 − $ 10 ) . If gambler wins the first game then gambler gains profit of $80 and has a total amount of $100. With this amount gambler can play 10 games which are lost. A total of 11 games are played. The second possibility that Y can take is LWLLLLLLLLL , because for playing the first game gambler spends $10, then gambler has $20 ( $ 30 − $ 10 ) . If gambler loses the first game then goes for second game, then gambler has $10 ( $ 20 − $ 10 ) . If gambler wins the second game gambler gains profit of $80 and has a total amount of $90. With this amount gambler can play 9 games which are lost. A total of 11 games are played. The third possibility that Y can take is LLWLLLLLLLL , because for playing the first game gambler spends $10, then gambler has $20 ( $ 30 − $ 10 ) . If gambler loses the first game then goes for second game, then gambler has $10 ( $ 20 − $ 10 )

Mathematical Statistics with Applications

7th Edition

ISBN: 9781111798789

Author: Dennis O. Wackerly

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 3, Problem 194SE

To determine

Find the probability that gambler wins exactly once before gambler loses initial capital if gambler commences with amount $30.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 193SE

Chapter 3, Problem 195SE

Students have asked these similar questions

In order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…

Problem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…

Chapter 3 Solutions

Mathematical Statistics with Applications

Ch. 3.2 - When the health department tested private wells in...Ch. 3.2 - You and a friend play a game where you each toss a...Ch. 3.2 - A group of four components is known to contain two...Ch. 3.2 - Consider a system of water flowing through valves...Ch. 3.2 - A problem in a test given to small children asks...Ch. 3.2 - Five balls, numbered 1, 2, 3, 4, and 5, are placed...Ch. 3.2 - Each of three balls are randomly placed into one...Ch. 3.2 - A single cell can either die, with probability .1,...Ch. 3.2 - In order to verify the accuracy of their financial...Ch. 3.2 - A rental agency, which leases heavy equipment by...

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Find the probability that gambler wins exactly once before gambler loses initial capital if gambler commences with amount $30.

Solution Summary: The author analyzes the probability that gambler wins exactly once before losing initial capital if he or she commences with 30.

Concept explainers

Videos

Find the probability that gambler wins exactly once before gambler loses initial capital if gambler commences with amount $30.

Want to see the full answer?

Chapter 3 Solutions