# Ex.15.2 Q5 Probability Solution - NCERT Maths Class 10

## Question

A jar contains \(24 \) marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is \(2/3\)· Find the number of blue balls in the jar.

## Text Solution

**What is known?**

A jar contains \(24\) marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is \(2/3\).

**What is the unknown?**

The number of blue balls in the jar.

**Reasoning:**

It is given in the question that total number of balls are \(24\). suppose the number of green marbles be x. Now to find the number of blue balls, subtract the green balls from the total number of marbles i.e. number of blue balls are \(24 – x\). It is given in the question that probability of getting green ball is \(\begin{align}\frac{2}{3}\end{align}\) , probability of getting green ball \(\begin{align}=\frac{2}{3}\end{align}\)

Put the values in the above and you will get the value of \(x\) i.e. the number of blue balls.

**Steps:**

Total number of marbles = \(24\)

Let the green marbles be \(x\) and the blue colour marbles be \(24 -x\)

Probability of getting green marbles \( \begin{align}=\frac{2}{3}\end{align}\)

\[\begin{align}\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } &=\frac{2}{3} \\ \frac{x}{24}&=\frac{2}{3} \\ x& =\frac{2}{3}\times 24 \\ x& =16 \end{align}\]

Therefore, the number of green marbles = \(16\)

Hence, total number of blue marbles

\(\begin{align} & =24-x \\ & =24-16=8 \\ \end{align}\)

Thus, the number of blue balls is \(8\).