Results 1 to 4 of 4

Math Help - Probability-taking from one box to another then drawing

  1. #1
    Newbie
    Joined
    Aug 2009
    From
    Morogoro
    Posts
    3

    Probability-taking from one box to another then drawing

    Hello, good day,
    Here is a thread to go about.
    The problem I faced is that no box has been specified please help.

    Question.
    The contents of two boxes are as follows; box A contains 3 red and 2 white balls, box B contains 2 red and 5 white balls. a box is selected at random, a ball is drawn and put into second box, and then a ball is drawn from the second box. Find the probability that both balls drawn are of the same colour.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Brain Exploder View Post
    Hello, good day,
    Here is a thread to go about.
    The problem I faced is that no box has been specified please help.

    Question.
    The contents of two boxes are as follows; box A contains 3 red and 2 white balls, box B contains 2 red and 5 white balls. a box is selected at random, a ball is drawn and put into second box, and then a ball is drawn from the second box. Find the probability that both balls drawn are of the same colour.
    Suppose the first ball is chosen from A now you can calculate the probability that they are both the same colour.

    Now instead; suppose the first ball is chosen from B, now you can calculate the probability that they are both the same colour.

    These two cases occur with equal probability so you can combine the results in the appropriate manner to get the final answer.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2009
    Posts
    17
    I'm not 100% certain, but l'll take a crack at it.

    r_A = red chosen from bucket A
    w_A = white chosen from bucket A
    r_B = red chosen from bucket B
    w_B = white chosen from bucket B

    P(same color)
    = (1/2) * P(a ball is chosen from A first and a ball from B is same color) +
    (1/2) * P(a ball is chosen from B first and a ball from A is same color)

    P(a ball is chosen from A first and a ball from B is same color)
    = P(r_A and r_B) + P(w_A and w_B)
    = P(r_A) * P(r_B) + P(w_A) * P(w_B)
    = (3/5)(3/8) + (2/5)(6/8)

    P(a ball is chosen from B first and a ball from A is same color)
    = P(r_B and r_A) + P(w_B and w_A)
    = P(r_B) * P(r_A) + P(w_B) * P(w_A)
    = (2/7)(4/6) + (5/7)(3/6)

    => P(same color)
    = (1/2)((3/5)(3/8) + (2/5)(6/8)) + (1/2)((2/7)(4/6) + (5/7)(3/6))
    = .53631
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,957
    Thanks
    1780
    Awards
    1
    Quote Originally Posted by doolindalton View Post
    I'm not 100% certain, but l'll take a crack at it.

    r_A = red chosen from bucket A
    w_A = white chosen from bucket A
    r_B = red chosen from bucket B
    w_B = white chosen from bucket B

    P(same color)
    = (1/2) * P(a ball is chosen from A first and a ball from B is same color) +
    (1/2) * P(a ball is chosen from B first and a ball from A is same color)

    P(a ball is chosen from A first and a ball from B is same color)
    = P(r_A and r_B) + P(w_A and w_B)
    = P(r_A) * P(r_B) + P(w_A) * P(w_B)
    = (3/5)(3/8) + (2/5)(6/8)

    P(a ball is chosen from B first and a ball from A is same color)
    = P(r_B and r_A) + P(w_B and w_A)
    = P(r_B) * P(r_A) + P(w_B) * P(w_A)
    = (2/7)(4/6) + (5/7)(3/6)

    => P(same color)
    = (1/2)((3/5)(3/8) + (2/5)(6/8)) + (1/2)((2/7)(4/6) + (5/7)(3/6))= .53631
    Although I did not do the calculation, the part in blue is correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: December 11th 2011, 11:05 AM
  2. Probability of drawing cards.
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: September 17th 2010, 06:42 PM
  3. Probability (drawing cards out of a set of 52)
    Posted in the Statistics Forum
    Replies: 3
    Last Post: July 20th 2010, 04:36 AM
  4. Probability(drawing cards)
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 3rd 2010, 01:07 PM
  5. probability (drawing balls from a bag)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 22nd 2010, 05:35 AM

Search Tags


/mathhelpforum @mathhelpforum