1.

A jar contains 54 marbles, each of which some are blue, some are green and same 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»

The total number of marbles = 54

It is given that,

P(getting a white marble) be x.

Since, there are only 3 types of marbles in the jar, the sum of probabilities of all three marbles must be 1.

Therefore, \(\frac{1}3\) + \(\frac{4}9\) + x = 1

⇒ \(\frac{3+4}9\) + x = 1

⇒ x = 1 - \(\frac{7}9\)

⇒ x = \(\frac{2}9\)

Therefore, p(getting a white marble) = \(\frac{2}9\).......(1)

Let the number of white marbles be n.

then, P(getting a white marbles) = \(\frac{n}{54}\)........(2)

from (1) and (2).

\(\frac{n}{54}\) = \(\frac{2}9\)

⇒ n = \(\frac{2\times54}9\)

⇒ n = 12

Thus, there are 12 white marbles in the jar.


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