# Ex.15.2 Q3 Probability Solution - NCERT Maths Class 10

## Question

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, determine the number of blue balls in the bag.

## Text Solution

**What is known? **

A bag contains \(5\) red balls and some blue balls and the probability of drawing a blue ball is double that of a red ball*.*

**What is unknown? **

The number of blue balls in the bag.

**Reasoning:**

First find out the total number of outcomes and all the possible outcomes. Now, to find the probability use the formula given below

\[\begin{align}\text{ Probability }=\frac{\text{No of possible outcomes}}{\text{ Total no of outcomes }} \\\end{align}\]

As it is given in the question that the probability of drawing a blue ball is double that of a red ball, that means

\(2 \times\)probability of drawing red ball = probability of drawing blue ball.

Substitute the values in the above and you can find out the number of blue balls.

**Steps:**

No of red balls \(= 5 \)

Let the no of blue balls be \(x\)

Total number of balls \(= x+5\)

Probability of drawing red ball

\[\begin{align}&= \frac{\text{ No of possible outcomes }}{\text{ Total no of outcomes }} \\&=\frac{5}{x+5}\end{align}\]

Probability of drawing blue ball

\[\begin{align}&= \frac{\text{ No of possible outcomes }}{\text{ Total no of outcomes }} \\&=\frac{x}{x+5}\end{align}\]

Thus, the probability of drawing a blue ball is double that of a red ball

\[\begin{align}2\left( \frac{5}{x+5} \right)=\frac{x}{x+5}\end{align}\]

Hence the number of blue balls \(= 10\)