A lot of 20 bulbs contains 4 defective pieces. One bulb is drawn at random from the lot. What is the probability that this bulb is defective ?

Question

Accepted Answer

To determine the probability that a randomly drawn bulb from the lot is defective, we need to consider the total number of bulbs and the number of defective bulbs in the lot.

1. **Total number of bulbs in the lot:** 20
2. **Number of defective bulbs:** 4

The probability of drawing a defective bulb is calculated by dividing the number of defective bulbs by the total number of bulbs:

$$
\text{Probability of defective bulb} = \frac{\text{Number of defective bulbs}}{\text{Total number of bulbs}} = \frac{4}{20}
$$

Simplifying the fraction $\frac{4}{20}$:

$$
\frac{4}{20} = \frac{1}{5}
$$

Thus, the probability that a randomly drawn bulb is defective is $\frac{1}{5}$.

**Explanation for why Option 3 is correct:**

- Option 3 is $\frac{1}{5}$, which matches the calculated probability of drawing a defective bulb from the lot. This confirms that Option 3 is indeed the correct answer.

**Explanation for why the other options are incorrect:**

- **Option 1: $\frac{1}{6}$** - This option is incorrect because it does not match the calculated probability of $\frac{1}{5}$. The fraction $\frac{1}{6}$ would imply a different number of defective bulbs or total bulbs, which is not the case here.

- **Option 2: $\frac{1}{4}$** - This option is incorrect because it suggests a higher probability than the actual $\frac{1}{5}$. The fraction $\frac{1}{4}$ would imply that there are 5 defective bulbs out of 20, which is not true.

- **Option 4: $\frac{2}{5}$** - This option is incorrect because it suggests an even higher probability than $\frac{1}{5}$. The fraction $\frac{2}{5}$ would imply that there are 8 defective bulbs out of 20, which is incorrect.

In conclusion, the correct probability of drawing a defective bulb from the lot is $\frac{1}{5}$, making Option 3 the correct choice.