Question

A jar contains $54$ marbles, each of which some are blue, some are green and some are white, the probability of selecting a blue marble at random is $\frac{1}{3}$ and the probability of selecting a green marble at random is $\frac{4}{9}$. How many white marbles does the jar contain?

Answer 1

Total number of marbles in the jar $=54$.

Probability of drawing a blue marble $=\frac{1}{3}$
We know that,

Probability of choosing a blue marble, $P\left(B\right)=\frac{\text{Number of blue marbles}}{\text{Total number of marbles}}$

$\Rightarrow \frac{1}{3}=\frac{\text{Number of blue marbles}}{54}$
$\Rightarrow \text{Number of blue marbles}=54\times \frac{1}{3}=18$

Probability of drawing a green marble $=\frac{4}{9}$

Similarly,

Probability of choosing a green marble, $P\left(G\right)=\frac{\text{Number of green marbles}}{\text{Total number of marbles}}$

$\Rightarrow \frac{4}{9}=\frac{\text{Number of green marbles}}{54}$

$\Rightarrow \text{Number of green marbles}=54\times \frac{4}{9}=24$

So, number of white marbles $=$ Total number of marble $-$ (Sum of blue and green marbles)

$=54-(18+24)=54-42=12$

Therefore, jar contain $12$ marbles.