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Discrete Distributions

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data

    At a school sports day, the timekeeping group for running events consists of 1 chief judge, 1 referee and 10 timekeepers. The chief judge and the referee are chosen from 5 teachers while the 10 timekeepers are selected from 16 students.

    (a) How many different timekeeping groups can be formed?
    (b) If it is possible to have a timekeeping group with all the timekeepers being boys, what are the possible numbers of boys among the 16 students?
    (c) If the probability of having a timekeeping group with all the timekeepers being boys is 3 / 364, find the number of boys among the 16 students.

    (Answers:
    (a) 160160;
    (b) 10, 11, 12, 13, 14, 15, 16
    (c) 12)

    2. Relevant equations

    Formulae for Bernoulli, Binomial, Geometric & Poisson Distributions

    3. The attempt at a solution

    I don't know how to solve part (c) of the question.

    I tried:

    xC10 / 16C10 = 3 / 364

    and x can be found as 12.

    I don't know if the above method is correct or not.

    However, the question should be solved using the distribution formulae.

    Another attempt:

    x: number of boys within the 16 students

    P(Boys) = x / 16

    16C10 (x / 16)10 (1 - x / 16)6 = 3 / 364

    But the x found is not correct.

    Can anyone tell me how to solve it?

    Thank you very much!
     
    Last edited: Mar 31, 2009
  2. jcsd
  3. Mar 31, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    I think the second attempt is wrong, because you are using the binomial distribution there (why doesn't it apply?)

    The first approach, although possible not worked out entirely correct, seems better. So let x be the number of boys in 16 students. You have to choose 10 students from the 16. What is the probability that they are all boys?
     
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