From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

Explanation

To find the probability distribution of the number of defective bulbs when drawing 4 bulbs from a lot of 30 bulbs (which includes 6 defectives) with replacement, we can follow these steps:

### Step 1: Define the Random Variable
Let \( X \) be the random variable representing the number of defective bulbs drawn in the sample of 4 bulbs.

### Step 2: Identify the Probabilities
Since there are 6 defective bulbs out of a total of 30 bulbs, the probability of drawing a defective bulb (denoted as \( p \)) is:
\[
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