When a certain basketball player takes his first shot in a game he succeeds with probability 1/2. If he misses his first shot, he loses confidence and his second shot will go in with probability 1/3. If he misses his first 2 shots then his third shot will go in with probability 1/4. His success probability goes down further to 1/5 after he misses his first 3 shots. If he misses his first 4 shots then the coach will remove him from the game. Assume that the player keeps shooting until he succeeds or he is removed from the game. Let X denote the number of shots he misses until his first success or until he is removed from the game. Compute Var(X)

When a certain basketball player takes his first shot in a game he succeeds with probability 1/2. If he misses his first shot, he loses confidence and his second shot will go in with probability 1/3. If he misses his first 2 shots then his third shot will go in with probability 1/4. His success probability goes down further to 1/5 after he misses his first 3 shots. If he misses his first 4 shots then the coach will remove him from the game. Assume that the player keeps shooting until he succeeds or he is removed from the game. Let X denote the number of shots he misses until his first success or until he is removed from the game. Compute Var(X)

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...

See similar textbooks

Similar questions

A loan officer knows that 18% of the bank’s mortgage holders will lose their jobs anddefault on their loan in the course of 5 years. She also knows that 22 % of the banksmortgage holders will lose their job within this period. Given that one of the mortgageholders just lost their jobs what is the probability that he will now default on the loan?
According to the survey of American households, the probability that the household owns Smart 3D HDTV if the house has two earning members is 51%. Of the households surveyed, 47% did not have two earning members and 48%had Smart 3D HDTVs. The probability that a household does not have two earning members and does not own a Smart 3D HDTV is
You are the webmaster for your firm's website. From your records, you know that the probability that a visitor will buy something from your firm is 0.26. In one day, the number of visitors is 1050. If the visitors' traffic is more than the expected for the day, what is the probability that at least 10 more than the expected visitors will buy something from the firm?
Imagine an animal that shows two variants; one long-legged and one short-legged. Each female produces 2 female offspring per generation and then dies. The offspring of the long-legged ones survive to adulthood (reproductive age) with a probability of 55% and the offspring of the short-legged ones survive to adulthood with a probability of 45%. If you begin with a population of 60 females of each type, what proportion of individuals will have long legs in 5 generations? (Note that you can ignore males and count only females and their offspring.) Show all work.
A person rides uber 30% of the time, her roommate gives her a ride 30% of the time and she rides with her mom 40% of the time. She is late 10% of the time with her roommate she is late 3% of the time when she rides uber and 7% of the time when she rides with her mom. What is the probability that she wil be on time if she rides with her roommate?
An outdoor basketball tournament consists of 3 days, from 7 April to 9 April. The weather of each day in April is classified as either sunny or rainy. The probability that 1 April is rainy is 0.5. The probability that a sunny day follows a sunny day is 0.75. The probability that a sunny day follows a rainy day is 0.25. Find the probability that 3 days is sunny in the tournament period.
On average there are 3 leaks for every 100 miles of a pipeline. What is the probability that a 50-mile section of the pipeline has at least 1 leak?
In a football match, there is a new striker on the Juventus side. The probability that the new striker will score goal today is three times higher than scoring none. Rakin and his friends are watching this match. Rakin tells his friends that the new striker is left footed as he read about him in an article; but, some friends are not believing him. The match is about to start and on the screen there is a note saying opponent defenders of Juventus are strong against right footed strikers. So, the probability of the striker being left footed will be five times higher if the striker scores a goal than scoring none. When match started, Rakin and his friends saw that the new striker is left footed. What is the probability that the striker will score today?
In a city, there are two independent firetrucks, the probability that the first firetruck access to the fire place during ten minutes is 0.75, while the probability that the second firetruck access the fire place during ten minutes is 0.6. what is the probability that both firetrucks can access the fire place at the same time?