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 $\frac{2}{3}$. Find the number of blue marbles in the jar.

• A. 12
• B. 16
• C. 11
• D. 8

Answer 1

The correct option is D

8

$\text{Given: P(green marble)}=\frac{2}{3}$

Since there are 24 marbles, therefore the sample space will be 24 (i.e. the denominator must be 24.)

$\text{Let us assume there are}\text{x}\text{number of}\text{green marbles in the jar.}$

$\text{For an event E, probability}P\left(E\right)=\frac{\text{Number of outcomes favorable to E}}{\text{Number of all possible outcomes of the experiment}}$
$\Rightarrow \text{P(green marbles)}=\frac{2}{3}=\frac{\text{x}}{24}$
$\Rightarrow \text{x}=16$

It implies that there are 16 green marbles in a jar of 24 marbles.
$\therefore \text{Number of blue marbles}=24-16=8.$