A bag contains one counter, known to be either white orblack. A white counter is put in, the bag is shaken, and a counteris drawn out, which proves to be white. What is now the chance ofdrawing a white counter? [Notice that the state of the bag, after theoperations, is exactly identical to its state before.]

A bag contains one counter, known to be either white or black. A white counter is put in, the bag is…

Answered: A bag contains one counter, known to be…

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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You are one space short of winning a baord game and must roll a 1 on a die to claim victory. You want to know how many rolls it might take. How would you simulate rolling the die until you get a 1?
Suppose a person is thinking about entering a MarioKart competition at theirlocal videogame store. The competition costs 20 dollars to enter. The competition consists of 10 matches. The person knows that their chance of winning each match is 65% and that each match is independent of the others. The payout for the competition is: WIN ALL 10 Matches: 500 Dollar Prize WIN 9 Matches: 250 Dollar PrizeWIN 8 Matches: 50 Dollar Prize OTHERWISE: Nothing 1) Suppose that this person enters the competition 5 times.What is the probability they break even?(Hint: To break even they would need to win the $50 prize twice and lose the other three times. Use a modified binomial to calculate this probability.)
In craps which of the following scenarios is least likely? (Remember, for each roll you're rolling two dice, so rolling a 7" means any combination of dice that adds to 7.) A. Roll an 8 on the first roll, and an 8 on the second roll to win the game. B. Roll a 4 on the first roll, and a 7 on the second roll to lose the game. C. Roll a 7 on the first roll to win the game. D. Roll a 6 on the first roll, and a 6 on the second roll to win the game. O E. Roll a 2, 3, or 12 on the first roll to lose the game.
I was wondering if you could help me understand how to find the probability of failure of the entire deck system assuming that the failures of groups A, B and C are independent of each other and that the failures of sub-groups B1 and B2 are also independent of each other
A vending machine contains 1000 lollipops. Some of the lollipops are red, and the others are blue. You don’t know how many there are of each color. However, you do know that these two alternatives are equally likely. There are 900 blue lollipops and 100 red ones. There are 500 blue lollipops and 500 red ones. When you put a coin into the vending machine, it gives you a lollipop, chosen at random. Suppose that it gives you a blue lollipop. What is the probability that there are 900 blue lollipops and 100 red ones? Show how you got the answer.
In an experimental study, researchers had each of their participants bet on each game of a professional football season. In the contingency table below is some information from a random sample of 100 bets from this study placed on the Columbus Crush (picking them to win) during the last 14 games of the season (the Crush had 7 wins and 7 losses over that period). The table indicates, for each bet placed on the Crush, whether or not the team won and how the participant who placed the bet wagered the following week. Each bet is classified according to two variables: result of picking the Crush ("Crush won" or "Crush lost") and bet placed the following week ("Picked Crush to win" or "Picked Crush to lose"). In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, result of picking the Crush and bet placed the following week, are independent. Round your answers to two…
In an experimental study, researchers had each of their participants bet on each game of a professional football season. In the contingency table below is some information from a random sample of 100 bets from this study placed on the Columbus Crush (picking them to win) during the last 14 games of the season (the Crush had 7 wins and 7 losses over that period). The table indicates, for each bet placed on the Crush, whether or not the team won and how the participant who placed the bet wagered the following week. Each bet is classified according to two variables: result of picking the Crush ("Crush won" or "Crush lost") and bet placed the following week ("Picked Crush to win" or "Picked Crush to lose"). In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, result of picking the Crush and bet placed the following week, are independent. Round your answers to two…
Students in a class like to secretly use online calculators in their quizzes. There are three such online calculators favoured amongst the students: WolframAlpha (WA), Symbolab (S), and GeoGebra (GG). A student's favourite calculator changes from quiz to quiz according to the following rules: If a student likes WA best, then it is has a 50% chance of remaining their favourite for the next quiz; 25% of becoming S for the next quiz; and 25% of becoming GG for the next quiz. If a student likes S best, then it has a 50% chance of becoming WA for the next quiz, and a 50% chance of becoming GG for the next quiz. If a student likes GG best, then it has a 33.3% chance of becoming any of the three calculators for the next quiz. For the first quiz, there are 120 who count WA as their favourite; 80 who count S as their favourite; and 50 who count GG as their favourite. What is true about the fourth quiz? Choose one of the following: 1. 115 students favour WA; 52 students favour S; and 83…
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Suppose there is a 3-stage experiment that are pairwise independent (i.e. they’re all independent from eachother). If stage one has 5 outcomes stage two has 6 outcomes and stage three has 2 possible outcomes, howmany outcomes does the experiment itself have?
(Ch. 2.1) A library has 5 copies of a certain book in stock. Two copies (1 and 2) are first printings, and the other three (3,4 and 5) are second printings. A student finds these copies on a shelf and begins to examine in random order, stopping when he finds a second printing of the book. For example, one possible outcome is (5), and another is (2,1,3) (a) List the outcomes in the sample space 8. (b) Let A denote the event that exactly one book must be examined. What outcomes are in A? (c) Let B be the event that book 4 is the one selected. What outcomes are in B?
where the first outcome is one of X, Y, and Z, and the second outcome in each case is one of A and B. Use the following probabilities instead of those given in your text: Pr[X]=37 Pr[Y]=27Pr[Z]=27Pr[A|X]=45Pr[B|X]=15Pr[A|Y]=23Pr[B|Y]=13Pr[A|Z]=18Pr[B|Z]=78 Pr[(XorY)|B]=

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