A box contains 5 red and k blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is \(\frac{2}{3}\), find the value of k.
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Correct Answer: Option D
Explanation:
\(p(blue) = \frac{\text{no of blue balls}}{\text{total no of balls}}\)
= \(\frac{2}{3} = \frac{k}{k + 5}\)
\(3k = 2(k + 5) \implies 3k = 2k + 10\)
\(3k - 2k = k = 10\)
\(p(blue) = \frac{\text{no of blue balls}}{\text{total no of balls}}\)
= \(\frac{2}{3} = \frac{k}{k + 5}\)
\(3k = 2(k + 5) \implies 3k = 2k + 10\)
\(3k - 2k = k = 10\)