Probability

1. We have a bag that contains n red balls and n blue balls. At each of 2n rounds we remove one of the balls from the bag randomly, and place it in one of available n bins. At each round, each one of the balls that remain in the bag is equally likely to be picked, as is each of the bins, independent of the results of previous rounds. Let Nk be the number of balls in the k -th bin after 2n rounds, i.e., after all balls have been placed in the bins.

1. Find the probability that N1=0 , i.e., that the first bin is empty after all balls have been removed and placed into bins.

2. What is the PMF pN1(k) of N1 ?

3. What is the expected number of empty bins?

4. What is the probability that the ball picked in the third round is red?

5. Let Ri denote the event that i -th ball picked is red. Are the events R1 and R2 independent?

  1. 👍 4
  2. 👎 0
  3. 👁 2,413
  1. 1. ((n-1)/n)^n
    2. k!/(n-k)!*p^n*(1-p)^n-k
    3. n*((n-1)/n)^n
    4.
    5. No

    1. 👍 5
    2. 👎 20
  2. 1) ((n-1)/n)^n
    2) (n!/(n-k)!*k!)(1/n)^n(1-1/n)^n
    3) n*((n-1)/n)^n
    4) 4/5 = 0.8
    5) No

    1. 👍 0
    2. 👎 12
  3. Isnt ans for 1st and 3rd question have the power 2n since we have (n+n) balls and 2n draws for the same

    1. 👍 9
    2. 👎 0
  4. 3 = 1/2

    1. 👍 1
    2. 👎 1
  5. Cant get the 4/5=0.8 on the 4th. How do you get to this

    1. 👍 1
    2. 👎 0
  6. On 1st and 3rd I have 2n as power as well. There are 2n rounds.

    1. 👍 1
    2. 👎 0
  7. on 2 it should be 2n pick k. then imo

    2) (2n!/(2n-k)!*k!)(1/n)^2n(1-1/n)^2n-k

    1. 👍 1
    2. 👎 2
  8. Also found 1/2 for 3.

    1. 👍 0
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. College Math

    Four balls are selected at random without replacement from an urn containing four white balls and five blue balls. Find the probability of the given event. ‚Äč All of the balls are blue.

  2. Math

    A bag contains three black balls, four white balls and five red balls. Three balls are removed without replacement. What is the probability of obtaining a one of each colour b at least two red balls ?

  3. math

    An urn contains 10 red balls, 6 green balls, 15 orange balls, and 14 blue balls. If one ball is randomly drawn from the urn, what are the odds against the ball being red? State your answer as a ratio using a colon to separate the

  4. math

    A bag contains 8 blue and 2 red balls. Three balls are chosen at the same time at random from the bag. What is the probability that exactly two of the balls are the same colour?

  1. probability theory

    3 students; A, B and C, are in a swimming race. A and B have the same probability of winning and each is twice as likely to win as C. Find the probability that B or C wins the swimming race. 3) Given three boxes as follows: Box A

  2. Mathematics

    A basket contains 3 red balls 5 blue balls and 7 green balls. Two balls are picked one after the other without replacement find the probability that. (a) Both are red. (b) First is blue, the other is green. (c) One is blue, the

  3. Math

    Assume that you are drawing two balls without replacement from an urn that contains 13 green balls, 10 blue balls, and 1 red ball. What is the probability that you will draw a blue balls and a red ball?

  4. pshs

    three balls are drawn successively from a box containing 6 red balls,4white balls and 5 blue balls. find the probability that tare hey drawn in the order red,white and blue if each ball is replaced?

  1. Maths

    A contains some red and blue balls. There are four more red than blue balls. A ball is removed at random and replaced. A second ball is removed. The probability that the two balls are different colours is 21/50. How many balls are

  2. physics

    in a bag there are 20 red 30black 40 blue50 white balls. what is the minimum number of balls to be drawn without replacement so that you are certsin about getting 4 red,5 black,6 blue,7 white balls

  3. Probability

    A basket contains 3 red balls 5 blue balls and 7 green balls. Two balls are picked one after the other without replacement find the probability that. (a) Both are red. (b) First is blue, the other is green. (c) One is blue, the

  4. Probability

    A bag contains some balls of which 1/4 are red. Forty more balls of which 5 are red are added. If 1/5 of all the balls are red, how many balls was there originary?

You can view more similar questions or ask a new question.