A bag contains 3 red balls, 5 blue balls and some green balls. One ball is drawn at random. If the probability of drawing a green ball is \(\dfrac{1}{3}\), find the number of green balls in the bag. Also find the probability of drawing a red ball.

Q.5 (ii) A bag contains 3 red balls, 5 blue balls and some green balls. One ball is drawn at random. If the probability of drawing a green ball is \(\dfrac{1}{3}\), find the number of green balls in the bag. Also find the probability of drawing a red ball.

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc 10th Save WhatsApp Report

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Answer: 4 green balls; \(P(\text{red}) = \dfrac{1}{4}\)

Let the number of green balls be \(g\). Then \(n(S) = 3 + 5 + g = 8 + g\).

\(P(\text{green}) = \dfrac{g}{8 + g} = \dfrac{1}{3} \Rightarrow 3g = 8 + g \Rightarrow 2g = 8 \Rightarrow g = 4\).

So \(n(S) = 12\). Check: \(P(\text{green}) = \dfrac{4}{12} = \dfrac{1}{3}\).

\(P(\text{red}) = \dfrac{3}{12} = \dfrac{1}{4}\).

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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A bag contains 3 red balls, 5 blue balls and some green balls. One ball is drawn at random. If the probability of drawing a green ball is \(\dfrac{1}{3}\), find the number of green balls in the bag. Also find the probability of drawing a red ball.

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