A jar contains 54 marbles each of which is blue , green or white. The probability of selecting a blue marble at random from the jar is 1/3  and the probability of selecting a green marble at random is 4/9 . How many white marbles does the jar contain?                                                                                               (Ans:12)

Ans: Let there be b blue, g green and w white marbles in the marbles in the jar. Then, b + g + w = 54

∴ P (Selecting a blue marble) =     b/54

It is given that the probability of selecting a blue marble is 1/3 .

∴ 1/3 =  b/54  => b = 18

We have,

P(Selecting a green marble) = 4/9

=>  g/54  = 4/9

[Q P (Selecting a green marble) = 4/9 (Given)]

=> g = 24

Substituting the values of b and g in (i), we get

18 + 24 + w = 54 => w = 12