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 probabilities that both items chosen are defective

• A. $\frac{20}{495}$
• B. $\frac{19}{495}$
• C. $\frac{99}{495}$
• D. none of these

Answer 1

The correct option is B $\frac{19}{495}$

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 both items chosen are defective

$P(A\cap B)=P\left(A/B\right)P\left(A\right)=\frac{20}{100}\times \frac{19}{99}=\frac{19}{495}$