Question

A bag contains $4$ white balls and some red balls. If the probability of drawing a white ball from the bag is $\dfrac{2}{5}$, find the number of red balls in the bag.
A). $2$
B). $4$
C). $8$
D). $6$

Answer 1

In this question, given that a bag contains $4$ white balls and some red balls. Also the probability of drawing a white ball is given as $\dfrac{2}{5}$. Here we need to find the number of red balls in the bag. First we need to find the total number of balls in the bag.
Formula used:
$Probability = \dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

Complete step-by-step solution:
Given,
$\text{No. of white balls} = 4$
Let $W$ be the probability of drawing the white balls.
Also given,
$P\left( W \right) = \dfrac{2}{5}$
Let $x$ be the number of red balls.
$\text{Total number of balls} = \text{Number of white balls} +\text{Number of red balls}$
$\text{Total number of balls} = \ 4 + x$
Given that the probability of drawing the white balls is $\dfrac{2}{5}$
By using the probability formula,
We get,
$\dfrac{4}{4 + x} = \dfrac{2}{5}$
By cross multiplying,
We get,
$4 \times 5 = 2\left( 4 + x \right)$
By removing the parentheses,
We get,
$20 = 8 + 2x$
By moving constants to one side,
We get,
$20 – 8 = 2x$
By subtracting,
We get,
$2x = 12$
$x = \dfrac{12}{2}$
By dividing,
We get,
$x = 6$
Hence the number of red balls are $6$
Final answer :
There are $6$ red balls in the bag .
Option : D). $6$

Note: The concept used to find the number of red balls is probability in an experimental approach. The simple rule for the probability is the number of desired outcomes divided by the number of possible outcomes. The probability of an event lies between $0$ and $1$ . The probability of an event never occurs greater than $1$.