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...
We are to distribute n balls randomly into k boxes. What is the expected number of...
We are to distribute n balls randomly into k boxes. What is the expected number of empty boxes and the variance of the number of empty boxes?
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)
(a) How many ways are there to put twelve identical balls into four boxes numbered 1,...
(a) How many ways are there to put twelve identical balls into four boxes numbered 1, 2, 3, and 4? (b) How many ways are there to put n identical balls into k boxes numbered 1, 2, . . ., k?
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?
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?
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