Question 1178918: Three are 15 defective products in a box containing 60 products. If 4 products are selected at a random, what is the probability that 3 products are defective?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
 There are 15 defective products in a box containing 60 products. If 4 products are selected at a random,
what is the probability that 3 products are defective?
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These probability problems, related to COMBINATIONS, were solved at this forum UNCOUNTABLE number of times.
They all are treated in the same way.
We find first the number of elements in the space of events.
In this problem, this number is the number of all 4-element subsets in the set of 60 products
total =  = 487635 (for calculation, I use the COMBIN function of Excel COMBIN(60,4) and get the answer in one click)
Next, I calculate the number of "favorable" events.
It is the number of all 4-element subsets, that contain 3 defective products of 15 defective products
and 1 good product of remaining 60-15 = 45 products.
This number of favorable events is equal to  = 455*45 = 20475.
THEREFORE, the answer to the problem's question is
P =  =  =  = 0.042 (rounded). ANSWER
Solved.
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If you want to see a million of similar (and different) problems, llok into the lesson
- Elementary Probability problems related to combinations
- Elementary Probability problems related to combinations REVISITED
in this site.
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