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 the second box was chosen? What is the probability that the third box was chosen? ( be careful, these are conditional probabilities)
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b) You have three boxes. In the first box, there are 4 white
balls and 2...
2. A box contains 5 red balls, 7 white balls, and 8 black balls. Four balls...
2. A box contains 5 red balls, 7 white balls, and 8 black balls. Four balls are randomly chosen (without replace- ment). What is the probability that (a) 1 red ball, 2 white balls, and 1 black ball are chosen? (b) exactly two red balls are chosen? (c) the first chosen is black, the last three chosen are two white balls and one black ball?
Suppose that there is a white urn containing two white balls and three red balls and...
Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing three white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. The probability of the second ball being...
1. One box contains seven red balls and three green balls, and a second box contains...
1. One box contains seven red balls and three green balls, and a second box contains six red balls and four green balls. A ball is randomly selected chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and placed in the first box. a. What is the probability that a red ball is selected from the first box and a red ball is selected from the second box?...
1 One box contains seven red balls and three green balls, and a second box contains...
1 One box contains seven red balls and three green balls, and a second box contains six red balls and four green balls. A ball is randomly selected chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and placed in the first box. a. What is the probability that a red ball is selected from the first box and a red ball is selected from the second box?...
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...
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at ran...
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one bal 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...
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...
3. A box contains 10 red balls, 6 blue balls, and 4 white balls. We have...
3. A box contains 10 red balls, 6 blue balls, and 4 white balls. We have taken 2 balls from the box. What are probabilities that we have taken c) one red ball and one white ball b) at least one blue bal a) 2 blue balls d) no one red ball
4. *A box contains 3 white balls, 4 black balls, and 3 red balls. Consider selecting...
4. *A box contains 3 white balls, 4 black balls, and 3 red balls. Consider selecting 3 balls at random (a) What is the probability that you pick exactly one of each color when you select 3 balls from the box? (b) What is the probability that you pick exactly 2 white balls and 1 red ball? (c) What is the probability that at least one of the balls is white when you select 3 balls from the box?
An urn contains 4 white balls and 6 red balls. A second urn contains 6 white...
An urn contains 4 white balls and 6 red balls. A second urn contains 6 white balls and 4 red balls. An urn is selected, and the probability of selecting the first urn is 0.8. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.) (a) the probability that the urn selected...
2. A box contains 5 red balls, 7 white balls, and 8 black balls. Four balls are randomly chosen (without replace- ment). What is the probability that (a) 1 red ball, 2 white balls, and 1 black ball are chosen? (b) exactly two red balls are chosen? (c) the first chosen is black, the last three chosen are two white balls and one black ball?
Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing three white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. The probability of the second ball being...
1. One box contains seven red balls and three green balls, and a second box contains six red balls and four green balls. A ball is randomly selected chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and placed in the first box. a. What is the probability that a red ball is selected from the first box and a red ball is selected from the second box?...
1 One box contains seven red balls and three green balls, and a second box contains six red balls and four green balls. A ball is randomly selected chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and placed in the first box. a. What is the probability that a red ball is selected from the first box and a red ball is selected from the second box?...
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...
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one bal 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...
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...
3. A box contains 10 red balls, 6 blue balls, and 4 white balls. We have taken 2 balls from the box. What are probabilities that we have taken c) one red ball and one white ball b) at least one blue bal a) 2 blue balls d) no one red ball
4. *A box contains 3 white balls, 4 black balls, and 3 red balls. Consider selecting 3 balls at random (a) What is the probability that you pick exactly one of each color when you select 3 balls from the box? (b) What is the probability that you pick exactly 2 white balls and 1 red ball? (c) What is the probability that at least one of the balls is white when you select 3 balls from the box?
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