A box contains 20 defective items and 80 non-defective items. If two items are selected at random without replacement, what will be the probability that both items are defective? A. $$\frac{1}{5}$$ B. $$\frac{1}{{25}}$$ C. $$\frac{{20}}{{99}}$$ D. $$\frac{{19}}{{495}}$$

$$rac{1}{5}$$
$$rac{1}{{25}}$$
$$rac{{20}}{{99}}$$
$$rac{{19}}{{495}}$$

The probability of event A happening, then event B, is the probability of event A happening times the probability of event B happening given that event A already happened. In this case, event A is selecting one defective item and event B is selecting another defective item.

The probability of selecting one defective item is the number of defective items divided by the total number of items, $\frac{20}{100}$.

The probability of selecting another defective item after one defective item has already been selected is the number of defective items remaining divided by the total number of items remaining, $\frac{19}{99}$.

Therefore, the probability of selecting two defective items at random without replacement is $\frac{20}{100} \cdot \frac{19}{99} = \boxed{\frac{19}{495}}$.

Option A is incorrect because it is the probability of selecting one defective item. Option B is incorrect because it is the probability of selecting two defective items with replacement. Option C is incorrect because it is the probability of selecting one defective item and one non-defective item.

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