Question

A jar contains 24 marbles of which some are green and others are blue. If a marble is drawn randomly from the jar, the probability that it is green is $\frac{2}{3}$. Find the probability of picking a blue marble. Using that, find the number of marbles of both kind.

Answer 1

Given,

Total number of marbles =24

P(green marbles)$=\frac{2}{3}$

We know that,

P(green marbles) + P(blue marbles) =1

Because the sum of probabilities of an event and its complementary event is always 1.

$\Rightarrow$ P(blue marbles) = 1 - P(green marbles) =$1-\frac{2}{3}=\frac{1}{3}$

Therefore, P(blue marbles) $=\frac{1}{3}$

Now, probability $\times$ total outcomes = favourable outcomes
$\Rightarrow$ Number of blue marbles = P(blue marbles) $\times$ 24
$\Rightarrow$ $\frac{1}{3}$ $\times$ 24 = 8

And, number of green marbles = 24 - 8 = 16,
or, $\Rightarrow$ Number of green marbles = P(green marbles) $\times$ 24
$\Rightarrow$ $\frac{2}{3}$ $\times$ 24 = 16