A box has 5 blue and 4 red balls. One ball is drawn at random and replaced. Its colour is also not noted. Then, another ball is drawn at random. What is the probability of second ball being blue?

Answer

To solve the problem of finding the probability of the second ball being blue after drawing a ball from a box containing 5 blue and 4 red balls, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Balls**:
- The box contains 5 blue balls and 4 red balls.
- Total number of balls = Number of blue balls + Number of red balls = 5 + 4 = 9.

2. **Understand the Process of Drawing Balls**:
- A ball is drawn at random and then replaced. This means that the total number of balls remains the same for the second draw.
- Since the first ball is replaced, the outcome of the first draw does not affect the second draw.

3. **Determine the Probability of Drawing a Blue Ball**:
- The probability of drawing a blue ball is given by the formula:
\[ P(\text{Blue}) = \frac{\text{Number of Blue Balls}}{\text{Total Number of Balls}} \]
- Substituting the values:
\[ P(\text{Blue}) = \frac{5}{9} \]

4. **Conclusion**:
- The probability of the second ball being blue is \( \frac{5}{9} \).

### Final Answer:
The probability of the second ball being blue is \( \frac{5}{9} \).

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