From a lot of 10 items containing 3 defectives, a sample of 4 items id drawn at random. Let the random variable X denote the number of defective items in the sample. If the sample is drawn randomly, find (i) the probability distribution of X (ii) `P(Xlt=1)` (iii) `P(X<1)` (iv) `P(0ltXlt2)`

Explanation

To solve the problem step by step, we will first calculate the probability distribution of the random variable \( X \), which represents the number of defective items in a sample of 4 drawn from a lot of 10 items (3 defective and 7 non-defective).

### Step 1: Define the Random Variable \( X \)

The random variable \( X \) can take values from 0 to 3, since there are only 3 defective items in the lot. Thus, the possible values of \( X \) are:
- \( X = 0 \): No defective items in the sample.
- \( X = 1 \): One defective item in the sample.
- \( X = 2 \): Two defective items in the sample.
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