Homework Answers
This can happen in 4 ways.
(a) placing white ball from Box 1 to Box 2 and then placing a white
ball from Box 2 to Box 1.
Prob.(black ball from Box 1) = b1/(b1 + w1).
(b) placing white ball from Box 1 to Box 2 and then placing a black
ball from Box 2 to Box 1.
Prob.(black ball from Box 1) = (b1 + 1)/(b1 + w1).
(c) placing black ball from Box 1 to Box 2 and then placing a white
ball from Box 2 to Box 1.
Prob.(black ball from Box 1) = (b1 - 1)/(b1 + w1).
(d) placing black ball from Box 1 to Box 2 and then placing a black
ball from Box 2 to Box 1.
Prob.(black ball from Box 1) = b1/(b1 + w1).
Total probability = adding the above 4 probabilities = (4 *
b1)/(b1 + w1).
.
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5) Box 1 contains wi white balls and bi black balls. Box 2 contains w2 white...
5) Box 1 contains w white balls and b black balls. Box 2 contais white balls...
5) Box 1 contains w white balls and b black balls. Box 2 contais white balls and b2 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.
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...
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?
Box 1 contains a red balls and b white balls. Box 2 contains c red balls...
Box 1 contains a red balls and b white balls. Box 2 contains c red balls and d white balls. One ball is randomly drawn from Box 1 and put into Box 2, and then one ball is randomly drawn from Box 2 and put back in Box 1. Finally, one ball is drawn at random again from Box 2. Let X denote the number of red balls drawn from Box 2 the 2nd time. Write down the distribution of...
Probability question *A box contains 3 white balls, 4 black balls, and 3 red balls. Consider...
Probability question
*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?
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?
Urn I contains 5 white balls and 5 black balls. Urn II contains 7 white balls...
Urn I contains 5 white balls and 5 black balls. Urn II contains 7 white balls and 3 black balls. Under which of the following plans is the probability of getting two white balls the greatest? (a) Draw one ball from each urn. (b) Draw two balls from Urn I. (c) Put all 20 balls in one urn and then draw two.
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...
Below are three boxes containing black and white balls. The number of each color is noted...
Below are three boxes containing black and white balls. The number of each color is noted inside the box. Draw a ball from box 1 and place it in box 2. Then draw a ball from box 2 and place it in box 3. Finally, draw a ball from box 3. Box 1 5 white 4 black Box 2 4 white 3 black Box 3 2 white 2 black What is the probability that the last ball, drawn from box...
Below are three boxes containing black and white balls. The number of each color is noted...
Below are three boxes containing black and white balls. The number of each color is noted inside the box. Draw a ball from box 1 and place it in box 2. Then draw a ball from box 2 and place it in box 3. Finally draw a ball from box 3. Box 1 5 white 2 black Box 2 2 white 3 black Box 3 3 white 0 black a) What is the probability that the last ball, drawn from...
5) Box 1 contains w white balls and b black balls. Box 2 contais white balls and b2 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.
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...
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?
Probability question
*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?
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?
Urn I contains 5 white balls and 5 black balls. Urn II contains 7 white balls and 3 black balls. Under which of the following plans is the probability of getting two white balls the greatest? (a) Draw one ball from each urn. (b) Draw two balls from Urn I. (c) Put all 20 balls in one urn and then draw two.
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...
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