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 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 wi white balls and bi black balls. Box 2 contains w2 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.
6) Assume that we have n boxes and each one of them contains k white balls and n-k black balls. We choose a box at random and we choose two balls from it (after choosing the first one we are not allowed to put it back). Compute the probability that both balls are white.
6) Assume that we have n boxes and each one of them contains k white balls and n-k black balls. We choose a box at random and we choose two balls from it (after choosing the first one we are not allowed to put it back). Compute the probability that both balls are white.
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...
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...
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?
There are 3 black and 4 white balls in a box. One ball is taken out at random. If it is black, then two white balls are put back in the box. If it is white, then one black ball is put back in the box. After that procedure another ball is taken out of the box. What is the probability that the first ball taken was white is the second ball taken was white?
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...