Question

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

• A. \(10\)
• B. \(15\)
• C. \(20\)
• D. \(25\)
• E. \(30\)

Hint:

In probability comparison questions, define the unknown first, write both probabilities clearly, and then apply the given condition directly.

Answer 1

The Correct Option is A

Concept: Probability is given by: \[ P(E) = \frac{ \text{Favourable outcomes} }{ \text{Total outcomes} } \] Here we compare probability of drawing blue and red balls.

Step 1: Assume number of blue balls. Let the number of blue balls be: \[ x \] Given red balls: \[ 5 \] Therefore total balls: \[ x + 5 \]

Step 2: Write probabilities. Probability of drawing a red ball: \[ P(R) = \frac{5}{x+5} \] Probability of drawing a blue ball: \[ P(B) = \frac{x}{x+5} \]

Step 3: Use the given condition. Given: \[ P(B) = 2P(R) \] So, \[ \frac{x}{x+5} = 2 \left( \frac{5}{x+5} \right) \]

Step 4: Solve for \(x\). \[ \frac{x}{x+5} = \frac{10}{x+5} \] Thus, \[ x = 10 \] Hence, \[ \boxed{10} \] So the number of blue balls is: \[ \boxed{(A)\ 10} \]