Calculate the Probability of Accepting a Lot

[sauerdan]

Can someone help me figure out how to calculate the following problem? I am not looking just for the answer but want to understand the methodology to get it.
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The following double-sampling plan has been proposed for evaluating a lot of 50 pieces:

Sample: 1, Sample size: 3, Acceptance number: 0, Rejection number: 3

Sample: 2, Sample size: 3, Acceptance number: 2, Reject number: 3

Using only the addition and multiplication rules for probability, calculate the probability of accepting a lot that is 10% defective.
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I am trying to understand the process of finding the answer (which is 0.984)

Thank you,

 

[tkhunny]

Does Sample 1 make any sense? What do you do with 1 and 2?

You may wish to consider a binomial approach.

(p+q)^3 = p^3 + 3(p^2)q + 3pq^2 + q^3

If p = percent defective = 0.10
and q = 1-p = percent not defective = 0.90

p(0 defective) = p(3 not defective) = q^3 = 0.90^3
p(1 defective) = 3pq^2 = 3(0.10)(0.90^2)
etc.

With a sample fo only three, just build the whole distribution and answer ALL the questions. No need to do one at a time.