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Probability 2

  1. Mar 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Twenty balls labelled 1 through 20 are put in a box. Eight balls are randomly selected from the box without replacement. Let x denote the largest number selected.
    (a) Denote by m the smallest possible value of x. Write down the value of m.
    (b) Let k be any integer such that m<=k<=20. Express P(x<=k) in terms of k.
    (c) It is known that x>15. Find the probability that x is 16.

    (Answers:
    (a) 8
    (b) kC8 / 20C8
    (c) 0.0538)

    2. Relevant equations

    Probability Formulae

    3. The attempt at a solution

    I know how to solve parts (a) and (b) but not part (c).

    I tried part (c) as follows:
    P(x=16)
    = P(x<=16) - P(x<=15)
    = (16C8 - 15C8) / 20C8
    = 0.0511

    However, the answer is not correct.

    Can anyone tell me how to solve it?

    Thank you very much!
     
  2. jcsd
  3. Mar 22, 2009 #2
    Hi chrisyuen,

    You need to compute the conditional probability

    P(x=16|x>15) = P(x=16)/P(x>15)
     
  4. Mar 23, 2009 #3
    I got it!

    Thank you very much!
     
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