A lot contains 20 articles. The probability that the lot contains 2 defective articles is 0.4 and the probability that the lot
contains exactly 3 defective articles is 0.6. Articles are drawn
at random one by one without replacement and tested till all
the defective articles are found. The probability that the
testing procedure ends at the twelfth testing is
Text Solution
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The testing procedure may terminate at the twelfth testing in two mutually exclusive ways.
(I) When lot contains 2 defective articles,
(II) When lot contains 3 defective articles.
Consider the following events.
A = Testing procedure ends at the twelfth testing.
A 1 = Lot contains 2 defective articles.
A 2 = Lot contains 3 defective articles.
Required probability
Now, 
Probability that first 11 draws contain 10
non-defective and one defective and 12th draw contains a defective article.
And 
= Probability that first 11 draws contain 9 non defective and 2 defective articles and 12 th draw contains a defective article = 
Hence, required probability
.
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