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A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is \(\frac{2}{3}\) . Find the number of blue marbles in the jar.

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Given a jar contains 24 marbles. 

Therefore, total marbles in the jar = 24. 

Given that the probability of getting a green marble from the jar is \(\frac{2}{3}\) .

Let marbles are green in the jar. 

Therefore, the probability of getting a green marble from the jar

\(\frac{Total\,number\,of\, green\,marble}{Total\,number\,of\,marbles\in\,the\,air}= \frac{x}{24}.\)

Hence, \(\frac{x}{24}\) = \(\frac{2}{3}\) (∵ probability of getting a green marble is \(\frac{2}{3}\). (given))

⇒ = \(\frac{2}{3}\times 24\) = 2× 8 = 16. 

Since, jar contains either green marbles of blue marble. 

Therefore, the number of blue marbles in the jar 

= Total number of marbles in the jar – Total green marbles in the jar 

= 24 – 16 = 8. 

Hence, total 8 marbles are blue in the jar.

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