A bag contains balls of two colours , 3 black and 3 white .What is the minimum number of balls which must be drawn from the bag ,without looking so that among these are two of the same colour ?

Options

A. A)2
B. B)3
C. C)4
D. D)5

Answer

To solve the problem of determining the minimum number of balls that must be drawn from a bag containing 3 black balls and 3 white balls to ensure that at least two of the drawn balls are of the same color, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have a bag with 3 black balls and 3 white balls. We need to find out how many balls we must draw to guarantee that at least two of them are of the same color.

2. **Considering the Worst Case Scenario**: To ensure we have at least two balls of the same color, we should consider the worst-case scenario where we draw the maximum number of balls without getting two of the same color.

3. **Drawing the First Ball**: When we draw the first ball, it can be either black or white. Let's say we draw a black ball.

4. **Drawing the Second Ball**: When we draw the second ball, it could be either black (making a pair) or white. If we draw a white ball, we now have one black and one white ball.

5. **Drawing the Third Ball**: Now, when we draw the third ball, regardless of whether it is black or white, we will definitely have at least two balls of the same color. This is because we already have one of each color from the first two draws.

- If the third ball is black, we have 2 black balls.
- If the third ball is white, we have 2 white balls.

6. **Conclusion**: Therefore, to guarantee that we have at least two balls of the same color, we must draw a minimum of 3 balls.

### Final Answer:
The minimum number of balls that must be drawn to ensure that at least two are of the same color is **3**.

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