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.

1. 8
2. 16
3. 24
4. None of these

Answer 1

Correct Answer - Option 1 : 8

Formula used:

Probability of occurrence of the event:

P(E) =  \(\frac{n(E)}{n(S)}\)

Where,

n(E) = Number of favorable outcome

n(S) = Number of possible outcome

Calculation:

Given that,

Number of marbles

n(S)= 24

Let, the number of blue marbles are x.

Hence, 

Number of green marbles

n(E) = 24 - x

According to the question, the probability of drawing green marbles is \(\frac{2}{3}\).

⇒ p(E) = \(\frac{24-x}{24} =\frac{2}{3}\) 

⇒ 24 - x = 16

⇒ x = 8

Hence, number of blue marbles are 8.