Question

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, then determine the number of blue balls in the bag.

Hint:

When probabilities are in a ratio, use the total as the sum of parts to form a simple linear equation.

Answer 1

Step 1: Let the number of blue balls be $x$.
Total balls = \( 5 + x \).

Step 2: Write probability ratios.
\[ P(\text{Red}) = \dfrac{5}{5 + x}, \quad P(\text{Blue}) = \dfrac{x}{5 + x} \] Given that \( P(\text{Blue}) = 2 \times P(\text{Red}) \).

Step 3: Substitute the values.
\[ \dfrac{x}{5 + x} = 2 \times \dfrac{5}{5 + x} \Rightarrow x = 10 \]
Step 4: Conclusion.
Hence, the number of blue balls is 10.