A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag.

Answer

To solve the problem, we need to find the number of blue balls in the bag given that the probability of drawing a blue ball is thrice that of drawing a red ball.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the number of blue balls be \( x \).
- The number of red balls is given as 5.

2. **Calculate Total Balls**:
- The total number of balls in the bag is the sum of red and blue balls:
\[ \text{Total balls} = x + 5 \]

3. **Calculate the Probability of Drawing a Red Ball**:
- The probability of drawing a red ball is given by the formula:
\[ P(\text{Red}) = \frac{\text{Number of Red Balls}}{\text{Total Balls}} = \frac{5}{x + 5} \]

4. **Calculate the Probability of Drawing a Blue Ball**:
- The probability of drawing a blue ball is:
\[ P(\text{Blue}) = \frac{\text{Number of Blue Balls}}{\text{Total Balls}} = \frac{x}{x + 5} \]

5. **Set Up the Equation**:
- According to the problem, the probability of drawing a blue ball is thrice that of drawing a red ball:
\[ P(\text{Blue}) = 3 \times P(\text{Red}) \]
- Substituting the probabilities we calculated:
\[ \frac{x}{x + 5} = 3 \times \frac{5}{x + 5} \]

6. **Simplify the Equation**:
- Since the denominators are the same, we can multiply both sides by \( x + 5 \) (assuming \( x + 5 \neq 0 \)):
\[ x = 15 \]

7. **Conclusion**:
- Therefore, the number of blue balls in the bag is:
\[ x = 15 \]

### Final Answer:
The number of blue balls in the bag is **15**.

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