Question

A lot contains 20 articles. The probability that the lot contains exactly two defective articles is 0.4; and the probability that it contains exactly three defective articles is 0.6. Articles are drawn from the lot at random one by one without replacement until all the defective are found. What is the probability that the testing procedure stops at the twelfth testing?

Answer 1

Suppose A is the event that the testing procedure ends at the twelfth testing.

A₁ = {the event that the lot contains 2 defective}

A₂ = {the event that the lot contains 3 defective}