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  • An urn question

    THe following question is taken from one of the study manuals.

    An urn contains 4 red balls, 8 green balls, and 2 yellow balls. Five balls are randomly selected, with replacement, from the urn. What is the probability that 1 red ball, 2 green balls and 2 yellow balls will be selected.

    The choices were: (a) 3/512, (b) 192/7^5, (c) 15/512 (d) 8/143 (e) 960/7^5

    MY answer was: (4C1)(8C2)(2C2)/14^5. However, my answer did not match. Could you tell me what I have done wrong?

    HOw would this answer change if the question was sampling with replacement?

    Thank you.

  • #2
    Audia,

    I got "e" for this problem (960/7^5).

    Your solution is wrong because you're mixing up methods.

    First, you cannot do (4C1) etc because you're sampling WITH replacement in this problem. Your denominator (14^5) is correct though.

    Here's what I did-

    Successful event: "RGGYY" and the different arrangements.

    R means red ball, G is green and so on.

    P(red ball) = 4/14
    P(green) = 8/14
    P(yellow) = 2/14.

    Combine them and take arrangements into account-

    P(successful event) = [(4/14) (8/14)^2 (2/14)^2] 30 divided by 14^5

    Why 30? coz that represents the number of ways RGGYY can be arranged.

    Hope this makes sense!
    Last edited by magic; June 20 2005, 03:22 PM.

    Comment


    • #3
      Originally posted by magic
      Audia,

      I got "e" for this problem (960/7^5).

      Your solution is wrong because you're mixing up methods.

      First, you cannot do (4C1) etc because you're sampling WITH replacement in this problem. Your denominator (14^5) is correct though.

      Here's what I did-

      Successful event: "RGGYY" and the different arrangements.

      R means red ball, G is green and so on.

      P(red ball) = 4/14
      P(green) = 8/14
      P(yellow) = 2/14.

      Combine them and take arrangements into account-

      P(successful event) = [(4/14) (8/14)^2 (2/14)^2] 30

      Why 30? coz that represents the number of ways RGGYY can be arranged.

      Hope this makes sense!
      I agree with magic's approach. To clarify his/her last statement, the 30 comes from (5 P 5) / [(2 P 2) * (2 P 2)]. See if you can reason through why this is.

      Comment

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