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 $\dfrac{2}{3}$. Find the number of blue balls in the jar.

Answer 1

Hint: For solving this question, first we let the number of green marbles be x. The total number of marbles are 24. So, the number of blue Marbles are 24 - x. The probability of getting green marble is given. By using the formula of probability, we find the number of green marbles and blue marbles.
The formula of probability used in this question is given below:
$P\left( \text{Event} \right)=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Complete step-by-step solution -
According to the problem statement, the total number of marbles = 24.
Let, the number of green marbles be ‘x’, then the number of blue marbles will be 24 -x.
Also, the probability of getting a green marble is given as $\dfrac{2}{3}$.
P (Getting a green marble) $=\dfrac{\text{Number of green marbles}}{\text{Total number of marbles}}$
On putting total number of marbles = 24 and number of green marbles = x, we get
$\begin{align}
  & \dfrac{2}{3}=\dfrac{x}{24} \\
 & \Rightarrow x=\dfrac{24\times 2}{3}=16 \\
\end{align}$
So, the number of green marbles = 24.
Now, number of blue marbles = total number of marbles – number of green marbles
Number of blue marbles = 24 – 16 = 8.
Hence, the number of blue marbles in the jar are 8.

Note: Students can verify the obtained answer by calculating the individual probability of the event and then summing those events to get 1. Probability of getting a blue marble = $\dfrac{8}{24}=\dfrac{1}{3}$. Probability of getting a green marble = $\dfrac{16}{24}=\dfrac{2}{3}$. The sum of both the probability is 1. So, the obtained answer is correct.