We randomly distribute 5 identical balls to 3 distinct boxes numbered 1,2,3. Given that no box...
We randomly distribute 5 identical balls to 3 distinct boxes numbered 1,2,3. Given that no box is empty find the probability that box 1 contains 3 balls.
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We randomly distribute 5 identical balls to 3 distinct boxes
numbered 1,2,3. Given that no box...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and 6 blue boxes labelled 1 to 6, such that the blue be with label i and the red box with labeli receive the same number of balls, for every ie (1,2,3,4,5, 6}? [10 marks
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and...
Question 29 (4 points) Two boxes each contain five numbered balls: • Box 1 contains balls...
Question 29 (4 points) Two boxes each contain five numbered balls: • Box 1 contains balls with numbers 3, 3, 3, 4, 5 • Box 2 contains balls with numbers 1, 1, 2, 2, 2 (a) You will randomly select one ball from each box. Let X be the difference between the numbers selected from the first and second box. Find the probability distribution of X. You can simply list the probabilities for each possible value of X instead of...
(1) We are given 40 identical (indistinguishable) objects and we want to distribute them among 7...
(1) We are given 40 identical (indistinguishable) objects and we want to distribute them among 7 distinct (distinguishable) boxes such that the box 1 must contain at least 3, and at most 10 objects. Use generating function to find the number of ways to do that.
10. Use Rubber Balls in a Box Setup. Suppose 5 rubber balls are to be randomly...
10. Use Rubber Balls in a Box Setup. Suppose 5 rubber balls are to be randomly drawn out (all at once). Find the probability that the numbers on the rubber balls will be sequential (when, after drawing, the numbers are arranged lowest to highest). This is a short answer question. The correct answer is a fraction. It is NOT NECESSARY to simplify the answer. 11. Use Rubber Balls in a Box Setup. Suppose 3 rubber balls are to be randomly...
Three boxes each contain a number of billiard balls. One box contains only even-numbered balls, one...
Three boxes each contain a number of billiard balls. One box contains only even-numbered balls, one box contains only odd numbered billiard balls, and the third box contains a mixture of odd and even numbered balls. All the boxes are mislabeled. By selecting one ball from only one of the boxes, can you correctly label the three boxes? Explain why or why not.
4. A box contains N identical balls numbered 1 through N. Of these balls, n are...
4. A box contains N identical balls numbered 1 through N. Of these balls, n are drawn at -1 Xi a time. Let Xi , X2,···x, denote the numbers on the n balls drawn. Let S,- Find var(S)
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...
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 notation. (b) Find the probability of each of the following events: A: "the first box is empty" B: "the first two boxes are empty". C: "no box contains more than one ball". (c) Find the probabilities of events A, B and C when three balls...
1.23 A box contains n identical balls numbered 1 through n [Papoulis 1.1]. Suppose k balls...
1.23 A box contains n identical balls numbered 1 through n [Papoulis 1.1]. Suppose k balls are drawn in succession. a) what is the probability that m is the largest number drawn? b) what is the provability that the largest number drawn is less than or equal to m?
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...
From a box with 5 balls numbered from 1 to 5, we draw a ball 500...
From a box with 5 balls numbered from 1 to 5, we draw a ball 500 times with replacement. Approximate the probability that we will draw the ball with the number “1” less than 80 times.
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and 6 blue boxes labelled 1 to 6, such that the blue be with label i and the red box with labeli receive the same number of balls, for every ie (1,2,3,4,5, 6}? [10 marks
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and...
Question 29 (4 points) Two boxes each contain five numbered balls: • Box 1 contains balls with numbers 3, 3, 3, 4, 5 • Box 2 contains balls with numbers 1, 1, 2, 2, 2 (a) You will randomly select one ball from each box. Let X be the difference between the numbers selected from the first and second box. Find the probability distribution of X. You can simply list the probabilities for each possible value of X instead of...
10. Use Rubber Balls in a Box Setup. Suppose 5 rubber balls are to be randomly drawn out (all at once). Find the probability that the numbers on the rubber balls will be sequential (when, after drawing, the numbers are arranged lowest to highest). This is a short answer question. The correct answer is a fraction. It is NOT NECESSARY to simplify the answer. 11. Use Rubber Balls in a Box Setup. Suppose 3 rubber balls are to be randomly...
4. A box contains N identical balls numbered 1 through N. Of these balls, n are drawn at -1 Xi a time. Let Xi , X2,···x, denote the numbers on the n balls drawn. Let S,- Find var(S)
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 notation. (b) Find the probability of each of the following events: A: "the first box is empty" B: "the first two boxes are empty". C: "no box contains more than one ball". (c) Find the probabilities of events A, B and C when three balls...
1.23 A box contains n identical balls numbered 1 through n [Papoulis 1.1]. Suppose k balls are drawn in succession. a) what is the probability that m is the largest number drawn? b) what is the provability that the largest number drawn is less than or equal to m?
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...
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