There are 4 white and 3 black balls in a bag. Find the probability of drawing 2 white ball one by one without replacement.

Explanation

To find the probability of drawing 2 white balls one by one without replacement from a bag containing 4 white and 3 black balls, we can follow these steps:

### Step 1: Identify the total number of balls
In the bag, we have:
- 4 white balls
- 3 black balls

Total number of balls = 4 (white) + 3 (black) = 7 balls.

### Step 2: Calculate the probability of drawing the first white ball
The probability of drawing the first white ball (W1) is given by the ratio of the number of white balls to the total number of balls:
\[ P(W1) = \frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{4}{7} \]

### Step 3: Update the count after the first draw
After drawing the first white ball, we have:
- Remaining white balls = 4 - 1 = 3
- Remaining total balls = 7 - 1 = 6

### Step 4: Calculate the probability of drawing the second white ball
The probability of drawing the second white ball (W2) after having drawn the first white ball is:
\[ P(W2 | W1) = \frac{\text{Remaining white balls}}{\text{Remaining total balls}} = \frac{3}{6} = \frac{1}{2} \]

### Step 5: Calculate the combined probability of both events
Since we are drawing the balls one after the other without replacement, we multiply the probabilities of the two events:
\[ P(W1 \text{ and } W2) = P(W1) \times P(W2 | W1) = \frac{4}{7} \times \frac{1}{2} = \frac{4}{14} = \frac{2}{7} \]

### Final Answer
The probability of drawing 2 white balls one by one without replacement is:
\[ \frac{2}{7} \]

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