6. Consider an urn which contains red balls and green balls. Initially there is just one greenball and one red ball in the urn. At each time step a ball is chosen randomly from the urn:(i) If the ball is red, then it's returned to the urn with an additional red ball; (ii) if the ball isgreen, then it's returned to the urn with an additional green ball.Let Xp denote the number of red balls in the urn after n draws. Suppose after 100 draws,there are 70 red balls, that is X100 = 70. What is the expected number of red balls in theurn after another 100 draws, that is E[X200|X100 = 70]? Round your answer to the nearestinteger.Hint: consider Yn = Xn/(n + 2).%3D

Expectation According to the definition of expectation, if a stochastic variable takes two values…

Answered: 6. Consider an urn which contains red…

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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A 'bingo' card has 5 columns and 5 rows. The 5 columns are labeled B,I,N,G,O. The squares in the 'B' column contain numbers from 1-15, chosen randomly. The square in the 'I','N','G', and 'O' columns contain numbers from 16-30, 31-45,46-60, and 61-75 respectively. All numbers are chosen randomly. The square in the center of the card (in the I column) is marked 'Free'.Each player has a bingo card. The Bingo master has a pot containing 75 markers that correspond to the 75 possible markings of the Bingo squares--i.e. B1-B15,I16-I30,…O61-O75. He chooses markers randomly one by one without replacement, and calls out the letter and number. A player gets 'Bingo' if he gets 5 numbers in a row, or 5 numbers in a column, or 5 on the diagonal (note the '0' is the center is automatically filled).
A lottery will randomly choose a four digit number with the following procedure: 10 tiles each with the digit zero through nine is placed in a box. One tile will be drawn at random; this tile will be post to the side and will form the first digit of a number. A second tile will be drawn from the remaining tiles in the box; this one will be laid to the side and will be second digit. Continue until four digits have been chosen. how many four digit lottery numbers can one form this way?
How many ways are there to distribute A x Bx C blue balls to 4 people Muslum, Orhan, Ferdi, and Bergen if Ferdi and Bergen together get no more than A + B and Orhan gets at least 2
) Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother’s house. Unknown to the man, three of these can contains an incorrect mix of paint. For this weekend’s big project, the man randomly selects four of these 1-gallon cans to paint his mother’s living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability that a least one of the four can selected contains an incorrect mix of paint. A) 78182 B) 74545 C) 50909 D) 49091
Dr. Lawrence has minimized his wardrobe during the fall of 2020, since there's no reason to dress up fancy these days. He has three pairs of jeans, five sweatshirts, and four hats that he puts to regular use. If he were to select his outfit for the day at random, how many different jean-sweatshirt-hat combinations are there? 6.
Suppose that you must choose three people to meet with a customer. You have nine people to choose from. In how many different ways can you choose these three people?
Suppose Fred has 2 pairs of pants (blue and black) and 3 shirts (red, blue, and black). Which of the following represents all of the outfits Fred could make with these options?
At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time? (4) (0.32) (0.68) 1! 4! (0.32)¹ (0.68)³ O2(0.32)(0.68) (0.32) (0.68)³
1. Once a month, a man puts some money in a cookie jar. During the 1st month he has P10.50 and each month he adds P0.50 more into the jar. How much money was placed in the jar during the last month of the 4th year?2. The seats in a theater are arranged so that there are 70 seats in the 1st row, 72 seats in the 2nd row and so on for 30 rows altogether. How many seats in all are there in the theater?
Jennifer, Bridget, Sandra, Robertina, and Joycelyn have their birthdays on consecutive days, but not necessarily in that order. Jennifer’s birthday is as many days before Sandra’s as Bridget’s is after Joycelyn’s. Robertina is two days older than Joycelyn. Sandra’s birthday this year is on a Wednesday. On what days of the week are the birthdays of the other four this year?

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