Question

A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.

Answer 1

Hint: In this question we need to find the number of red balls in the bag using the simple probability formula. In order to solve it, we will start with assuming the number of red colour balls as x. This will help us solve the question easily.

Complete step-by-step answer:
We have been given a box with 12 balls, so let the number of red balls initially in the bag be x.
So, the probability of drawing a red ball is $= \dfrac{x}{{12}}$………………. Equation (1)
Now, we have added 6 red balls in the bag.
So, now the probability of drawing a red ball is $= \dfrac{{x + 6}}{{18}}$…………….. Equation (2)
Now, we have been given that the new probability is double the earlier one.

$\Rightarrow 2x = x + 6$
$\Rightarrow x = 6$
So, there were 6 red balls in the bag.

Note: Whenever we face such types of problems the key point to remember is that we need to have a good grasp over probability. In these types of questions, we should always compute the number of favourable outcomes and the sample space and then form the equations. This reduces the probability to make an error to solve the question.