A statistics Department had purchased 24calculators in which 4 are defective. Calculators are selected one-after-another without replacement and tested. What is the probability that the second calculator found to be defective is the eighth calculator selected.
Use the Hypergeometric distribution
The probability with "n=7, N=24, k=4"
"P(second\\ defective)=\\dfrac{\\dbinom{4}{1}\\dbinom{24-4}{7-1}}{\\dbinom{24}{7}}\\cdot\\dfrac{4-1}{24-7}"
"=\\dfrac{340}{759}\\cdot\\dfrac{3}{17}=\\dfrac{20}{253}"
The probability that the second calculator found to be defective is the eighth calculator selected is "\\dfrac{20}{253}."
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