There are two boxes. At first, each box contains one white ball and one black ball. At each step, we drawone ball from each box randomly and exchange them. If we set thatState 1 = Box 1 contains no white balls,State 2= Box 1 contains one white ball,State 3 = Box 1 contains two white balls.1. Find the transition matrix.Answer:2. After 10 steps, what is the probability that box 1 contains two white balls?Answer:Submit Question

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Answered: There are two boxes. At first, each box…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 6E

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Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month, a Brand A user has a 20 probability of switching to Brand B and a 5 of not using either brand. A Brand B user has a 15 probability of switching to Brand A and a 10 probability of not using either brand. A nonuser has a 10 probability of purchasing Brand A and a 15 probability of purchasing Brand B. How many people will be in each group a in 1 month, b in 2 months, and c in 18 months?
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Dylan, a high school senior has applied to four different colleges. These are MIT, Harvard, Princeton, and John Jay. Based upon his high school record he estimates that he has a .17 probability of being accepted at MIT, a .13 probability of being accepted at Harvard, a .10 probability of being accepted at Princeton, and a .59 probability of being accepted at John Jay. Because colleges do not communicate with one another in admissions, acceptance at one college is independence of acceptance at another school.a. What is the probability that Dylan is accepted at none of the four schools? b. What is the probability that Dylan is accepted at all four of the schools? c. What is the probability that Dylan is accepted in at least one of the four schools d. What is the probability that Dylan is accepted at both Harvard and Princeton? e. What is the probability that Dylan is accepted at either Harvard or Princeton? f. What is the probability that Dylan is only accepted at John Jay?
A city uses three pumps to carry water from a river to a reservoir. Pumps A and B are new, and have a probability of failing of 0.015 on any day. Pump C is older, and has a probability of failure of 0.08 on any day. Pumps A and B operate Monday-Friday. On Saturday, pumps A and C operate while pump B is serviced. On Sunday, pumps B and C operate while pump A is serviced. Answer the following questions, assuming that the pumps operate independently of one another, and independently from day to day. Determine the probability that pump A works on a day that it is in use. Find the probability that pumps A and B both fail on a day they are both in use. Compute the probability that at least one pump fails on any Sunday. Find the probability that pump A works, and C fails on any Saturday. Determine the probability that no pumps fail in a week.
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Please answer the following questions and write properly.
A soccer team has 2 games scheduled for one weekend. It has a 0.4 probability of not losing first game and 0.7 probability of not losing the second game, independent of the first. If the team doesn't lose a particular game, the team is equally likely to win or tie. The team will receive 2 points for a win, 1 for a tie, and 0 for a loss. Find the PMF of the number of points that the team earns over the weekend. Find the expected value for the number of points earned. Find the variance for the number of points earned.
Player A and Player B play chess (either of them wins, a draw is not permitted). If player A plays White, the probability of him/her winning is 0.72. If player A plays Black, the probability of him/her winning is 0.63. Player A and Player B play 2 games and in the second game, they change sides. Find the probability that player B wins both games.
When the store opens, Arish, Meera, and Zenobia enter. There are two service counters. Arish begins service at one counter, and Meera begins service at the other counter. Zenobia waits until either Arish or Meera finishes service, and then begins service at that point in time. Assume that the three service times are independent, exponentially distributed random variables. Arish's service time has mean 4 minutes, Meera's service time has mean 5 minutes, and Zenobia's service time has mean 6 minutes. (a) What is the probability that Arish completes service before Meera? (b) What is the expected time that Zenobia waits until starting service? (C) What is the probability that the three finish in alphabetical order?
Consider a system of four flipped coins. (&) What s the probability that two land heads and the other two tails? (b) Label the four coins 1.2, 3, and 4. Make a chart that lists the various possible configurations that have two heads and two tails. Is the number of configurations on your chart

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