# Homework Help: Probability choosing (non)defective items

1. Jun 9, 2010

### satchmo05

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. Jun 10, 2010

### CompuChip

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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