From a batch of $100$ items of which $20$ are defective, exactly two items are chosen, one at a time, without replacement. Calculate the probability that the first item chosen is defective.

\frac{20}{100}

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\frac{20}{120}

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\frac{2}{100}

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none of these

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Solution

The correct option is A $\frac{20}{100}$
Let $A$ ={first item chosen is defective}, $B$ ={second item chosen is defective}

Given:

Total number of items = $100$ .

NUmber of defective items = $20$

To find:

the probabilities that the first item is chosen is defective

$P (A) = \frac{Number of items defective}{total number of items} = \frac{20}{100} = \frac{1}{5}$

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