Homework Answers
probability that we draw red ball =P(1st urn and red ball+2nd urn and red ball+3rd urn and red ball+4th urn and red ball) =(1/4)*(1/10)+(1/4)*(2/10)+(1/4)*(3/10)+(1/4)*(4/10)=1/4 =0.25
Example. 2 urns. Red urn contains 3 red balls, 2 white balls. White urn contains 1...
Example. 2 urns. Red urn contains 3 red balls, 2 white balls. White urn contains 1 red ball, 4 white balls. Pick an urn randomly. Randomly select a ball from that urn. Without replacing the 1st ball, select a ball from the urn whose color matches the first ball. Q. Make a tree diagram, complete with probabilities describing this situation. Q. Find the probability that the first ball is white. Q. Find the probability that the second ball is white....
Five white balls and two red balls are distributed between two urns A and B in...
Five white balls and two red balls are distributed between two urns A and B in such a way that urn A contains 2 white balls and 2 red balls and urn B contains 3 white balls. At each step, we draw one ball from each urn and place the ball drawn from urn A into urn B and conversely with the ball from urn B. Find the long run proportion of time that urn A will contain 4 white...
Suppose we have two urns (a left urn and a right urn). The left urn contains N black balls and the right urn contains N red balls.
Suppose we have two urns (a left urn and a right urn). The left urn contains N black balls and the right urn contains N red balls. Every time step you take one ball (chosen randomly) from each urn, swap the balls, and place them back in the urns. Let Xm be the number of black balls in the left urn after m time steps. Find the Markov chain model and find the unique stationary distribution when N=5
One of two urns is chosen at random with one just as likely to be chosen...
One of two urns is chosen at random with one just as likely to be chosen as the other. Then a ball is withdrawn from the chosen urn. Urn 1 contains 5 white and 2 red balls, and urn 2 has 4 white and 3 red balls. If a white ball is drawn, what is the probability that it came from urn 1?
Consider 3 urns. The urn A contains 5 white balls and 10 red balls, the urn...
Consider 3 urns. The urn A contains 5 white balls and 10 red balls, the urn B contains 9 white balls and 6 red balls and the urn C contains 4 white balls and 9 red balls. A ball is selected from ballot box 1 and placed in ballot box 2, then one ball is taken from ballot box 2 and placed in ballot box 3. Finally, a ball is taken from ballot box 3. What is the probability that...
(1 point) One of two urns is chosen at random with one just as likely to...
(1 point) One of two urns is chosen at random with one just as likely to be chosen as the other. Then a ball is withdrawn from the chosen urn. Urn 1 contains 4 white and 5 red balls, and urn 2 has 3 white and 4 red balls. If a white ball is drawn, what is the probability that it came from urn 1? (Hint: Draw a tree diagram first) (1 point) In a random sample of 1,000 people,...
Urn 1 contains 3 red and 6 blue balls, and urn 2 contains 4 red and...
Urn 1 contains 3 red and 6 blue balls, and urn 2 contains 4 red and 3 blue balls. The urns are equally likely to be chosen. a) If a blue ball is drawn, what is the probability that it came from urn 1? b) If a red ball is drawn, what is the probability that it came from urn 2?
Need help with well-explained solution 1. Assume that there are two urns. The first urn contains...
Need help with well-explained solution 1. Assume that there are two urns. The first urn contains 4 red balls, 3 blue balls, and 3 white balls. The second urn contains 2 red balls, 4 blue balls, and 4 white balls. You randomly select an urn and take two balls from the urn. The probability that you pick the first urn is 40%. What is the probability that (a) the two balls are red? (b) the second ball is blue? (c)...
In the previous problem, 10 balls randomly dropped into 4 urns, and for j e1,4), Xj...
In the previous problem, 10 balls randomly dropped into 4 urns, and for j e1,4), Xj is the number of balls that fall into the jth urm We would like to determine expectations and variances of the Xj's. To do so, for i {1,...,10} and j E{1,...,4), let Tiy be the indicator variable that the ith ball falls into jth urn. For example, if the 8 th ball drops in urn 3, then T8,3-1 and T$4-0 Find: . Е (Ту)....
2, Five white balls and five black balls are distributed in two urns in such a...
2, Five white balls and five black balls are distributed in two urns in such a way that each urn contains five balls. At each step we draw one ball from each urn and exchange them. Let Xn be the number of white balls in the left urn at time n. Compute the transition probability for X,
Example. 2 urns. Red urn contains 3 red balls, 2 white balls. White urn contains 1 red ball, 4 white balls. Pick an urn randomly. Randomly select a ball from that urn. Without replacing the 1st ball, select a ball from the urn whose color matches the first ball. Q. Make a tree diagram, complete with probabilities describing this situation. Q. Find the probability that the first ball is white. Q. Find the probability that the second ball is white....
(1 point) One of two urns is chosen at random with one just as likely to be chosen as the other. Then a ball is withdrawn from the chosen urn. Urn 1 contains 4 white and 5 red balls, and urn 2 has 3 white and 4 red balls. If a white ball is drawn, what is the probability that it came from urn 1? (Hint: Draw a tree diagram first) (1 point) In a random sample of 1,000 people,...
In the previous problem, 10 balls randomly dropped into 4 urns, and for j e1,4), Xj is the number of balls that fall into the jth urm We would like to determine expectations and variances of the Xj's. To do so, for i {1,...,10} and j E{1,...,4), let Tiy be the indicator variable that the ith ball falls into jth urn. For example, if the 8 th ball drops in urn 3, then T8,3-1 and T$4-0 Find: . Е (Ту)....
2, Five white balls and five black balls are distributed in two urns in such a way that each urn contains five balls. At each step we draw one ball from each urn and exchange them. Let Xn be the number of white balls in the left urn at time n. Compute the transition probability for X,
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