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Homework Help: Probability choosing (non)defective items

  1. Jun 9, 2010 #1
    1. The problem statement, all variables and given/known data
    A set of 25 items contains 5 defective items. Items are sampled at random one at a time. What is the probability that the 3rd and 4th defectives occur at the 5th and 6th sample draws if the items are:
    a.) replaced after each is drawn?
    b.) not replaced after each is drawn?

    2. Relevant equations
    I s'pose I could use the binomial theorem, but in the section this problem is in - it has not been covered. I really do not know any other useful formulas.

    3. The attempt at a solution
    If I were to define my events, let A: chose non-defective item, and B: chose defective item. The probability, based on the first line of the problem, is P(A) = 0.8. From here, I do not know where to start.

    Any helpful hints that could get me going? Thank you for all help in advance!
  2. jcsd
  3. Jun 10, 2010 #2


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    Science Advisor
    Homework Helper

    Also note that the 3rd and 4th defective should be chosen at the 5th and 6th sample draw.

    So you will need at least
    1) the probability of choosing 2 defectives and 2 non-defectives in the first 4 draws
    2) the probability that the fifth and sixth are defective (in the second case, add: given that the first two draws contain two defective and two non-defective samples)
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