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, find the number of blue balls in the bag.
Step-by-Step Solution
Key Concept: Let blue balls be $x$. Total $= 5 + x$.<br>$P(\text{Blue}) = \dfrac{x}{5+x}, P(\text{Red}) = \dfrac{5}{5+x}$.<br>Given $\dfrac{x}{5+x} = 2 \times \dfrac{5}{5+x} \Rightarrow x = 10$.
$P(\text{Blue}) = \dfrac{x}{5+x}, P(\text{Red}) = \dfrac{5}{5+x}$. [1.0 Mark]
$x/(5+x) = 10/(5+x) \Rightarrow x = 10$. There are 10 blue balls. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Setting up probability equation: 1.0 Mark
Solving number of blue balls $= 10$: 1.0 Mark
Correct Answer: