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5. Three balls are placed at random in three boxes, with no restriction on the number of balls per box. (a) List the 27 equally probable outcomes of this experiment. Be sure to explain your notat...
b) You have three boxes. In the first box, there are 4 white balls and 2...
b) You have three boxes. In the first box, there are 4 white balls and 2 red balls. In the second box, there are only 10 red balls and in the third box, there are 10 red balls and 5 white balls. A red ball is extracted blindly from a box chosen at random, but you don’t know from which box the ball was extracted What is the probability that the first box was chosen? What is the probability that...
Michael has a box of colored balls. It contains two red balls, two green balls, two...
Michael has a box of colored balls. It contains two red balls, two green balls, two yellow balls, and five blue balls. Michael draws a ball at random from the box Let R denote the event that the ball he draws is red, and let B denote the event that the ball he draws is blue. What is Pr(R|B)? What is Pr(R|B′)? Enter your answers as whole numbers or fractions in lowest terms. A bag contains four 1-dollar bills, three...
In dynamic resource allocation r tasks are assigned at random to n computers, with no restriction...
In dynamic resource allocation r tasks are assigned at random to n computers, with no restriction on the number of jobs per computer; list the possible outcomes of this experiment. Be sure to explain your notation. Assuming that the outcomes are all equally probable, find the probability of each of the following events : "Computer number 1 is B: "Computers number 1 and 2 are assigned no jobs"; C:"exactly two of the computers are assigned no jobs" D: "No computer...
5) Box 1 contains w white balls and b black balls. Box 2 contains w white...
5) Box 1 contains w white balls and b black balls. Box 2 contains w white balls and b black balls. We take one ball from Box 1 and place it into Box 2. Then we take a ball from Box 2 and place it into Box 1. Finally we take a ball from Box 1. Compute the probability that this ball is black 6) Assume that we have n boxes and each one of them contains k white balls...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box number 2 contains two black and one white ball. Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one ball from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white. We are going to find MAP estimate for the...
5. Three boxes are numbered 1, 2 and 3. For k 1, 2, 3, box k contains k blue marbles and 5 - k red marbles. In a two-step experiment, a box is selected and 2 marbles are drawn from it without replace...
5. Three boxes are numbered 1, 2 and 3. For k 1, 2, 3, box k contains k blue marbles and 5 - k red marbles. In a two-step experiment, a box is selected and 2 marbles are drawn from it without replacement. If the probability of selecting box k is proportional to k, then the probability that two marbles drawn have different colours is 6. Two balls are.dropped in such a way that each ball is equally likely to...
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen...
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events A: One of the balls is yellow B: At least one ball is red h C: Both balls are green D:Both balls are of the same color ) Find the following conditional probabilities: (a) P(BA)- b) P(DB)- (c) P(DIC)-
(25) A game has two boxes as follows: Box A initially contains 2 white balls Box...
(25) A game has two boxes as follows: Box A initially contains 2 white balls Box B initially contains 3 red balls. At each step in the game, 1 ball is selected at random from each box and the 2 balls are interchanged. Thus, Box A always contains 2 balls, and Box B always contains 3 balls. The game continues indefinitely. The game may be described by a Markov chain having three states: S0,S1,S2, whose subscript denotes the number of...
lomework Assignments (1 point) A box contains one yellow, two red, and three green balls. Two balls are randomly chosen...
lomework Assignments (1 point) A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events: A: One of the balls is yellow B: At least one ball is red) C: i Both balls are green h D: I Both balls are of the same color Find the following conditional probabilities: a) P(BIA) b) P(BD)- Note: You can earn partial credit on this problem.
lomework Assignments (1 point) A box...
1. Each box below contains a number of red bells )and a number of white balls (w), as indicated: 6 T 2 w 3 r 2 r 5...
1. Each box below contains a number of red bells )and a number of white balls (w), as indicated: 6 T 2 w 3 r 2 r 5 w 4 w Box 1 Box 2 Box 3 A box is Cosen, with probability P(Box 1)-a, P(Box 2)-2, P(Box 3)-N; then a ball is chosen at random from that box. a. Find the probability that a red ball is choeen. b. Given that a red ball is chosen, find the probability...
In dynamic resource allocation r tasks are assigned at random to n computers, with no restriction on the number of jobs per computer; list the possible outcomes of this experiment. Be sure to explain your notation. Assuming that the outcomes are all equally probable, find the probability of each of the following events : "Computer number 1 is B: "Computers number 1 and 2 are assigned no jobs"; C:"exactly two of the computers are assigned no jobs" D: "No computer...
5) Box 1 contains w white balls and b black balls. Box 2 contains w white balls and b black balls. We take one ball from Box 1 and place it into Box 2. Then we take a ball from Box 2 and place it into Box 1. Finally we take a ball from Box 1. Compute the probability that this ball is black 6) Assume that we have n boxes and each one of them contains k white balls...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box number 2 contains two black and one white ball. Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one ball from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white. We are going to find MAP estimate for the...
5. Three boxes are numbered 1, 2 and 3. For k 1, 2, 3, box k contains k blue marbles and 5 - k red marbles. In a two-step experiment, a box is selected and 2 marbles are drawn from it without replacement. If the probability of selecting box k is proportional to k, then the probability that two marbles drawn have different colours is 6. Two balls are.dropped in such a way that each ball is equally likely to...
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events A: One of the balls is yellow B: At least one ball is red h C: Both balls are green D:Both balls are of the same color ) Find the following conditional probabilities: (a) P(BA)- b) P(DB)- (c) P(DIC)-
(25) A game has two boxes as follows: Box A initially contains 2 white balls Box B initially contains 3 red balls. At each step in the game, 1 ball is selected at random from each box and the 2 balls are interchanged. Thus, Box A always contains 2 balls, and Box B always contains 3 balls. The game continues indefinitely. The game may be described by a Markov chain having three states: S0,S1,S2, whose subscript denotes the number of...
lomework Assignments (1 point) A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events: A: One of the balls is yellow B: At least one ball is red) C: i Both balls are green h D: I Both balls are of the same color Find the following conditional probabilities: a) P(BIA) b) P(BD)- Note: You can earn partial credit on this problem.
lomework Assignments (1 point) A box...
1. Each box below contains a number of red bells )and a number of white balls (w), as indicated: 6 T 2 w 3 r 2 r 5 w 4 w Box 1 Box 2 Box 3 A box is Cosen, with probability P(Box 1)-a, P(Box 2)-2, P(Box 3)-N; then a ball is chosen at random from that box. a. Find the probability that a red ball is choeen. b. Given that a red ball is chosen, find the probability...
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