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Quantitative Aptitude

Introduction to Probability

In a pack the...

Question

In a pack there are $6$ articles out of which exactly three are defective. They are tested one by one till all the defective articles are found. The probability that it will take exactly $3$ tests is:

A

\frac{1}{10}

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B

\frac{1}{20}

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C

\frac{1}{5}

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D

\frac{1}{2}

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Solution

The correct option is B $\frac{1}{20}$
$\begin{matrix} o b a b i l i t y t h a t i t w i l l g o f o r e x c a t l y 3 t e s t m e a n s a l l d e f e c t i v e i t e m s a r e t a k e n i n 3 t e s t = \frac{3}{6} \times \frac{2}{5} \times \frac{1}{4} = \frac{1}{20} H e n c e, o p t i o n B i s t h e c o r r e c t a n s w e r . \end{matrix}$

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