Question

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.

• A. $\frac{20}{100}$
• B. $\frac{20}{120}$
• C. $\frac{2}{100}$
• D. none of these

Answer 1

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

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