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A box contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the box is $\frac{1}{3}$ and the probability of selecting a green marble at random is $\frac{4}{9}$ . What is the number of white marbles in the box?

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answer is B.

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Detailed Solution

Given, a box contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the box is

\frac{1}{3}

and the probability of selecting a green marble at random is

\frac{4}{9} .

We know that,

Probability of an event = Number of favourable outcomes Total number of outcomes

The total number of outcomes is given as 54.
Let the number of favourable outcomes for getting a blue marble be b.
Now, the probability of finding the blue marble is

b 54

Therefore,

13 = b 54

\Rightarrow

b is 18.
Let the number of favourable outcomes for getting a green marble be g
The probability of finding the green marble is

49

g 54 = 49

\Rightarrow

g is 24.
Let the number of favourable outcomes for getting a white marble be w.
Now, we can say that,

18 + 24 + w = 54 w = 12

So, the total number of marbles in the jar is 12 white marbles.
Hence, the correct option is 2.

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