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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 $\frac{1}{3}$, and the probability of selecting a green marble at random is $\frac{4}{9}$. How many white marbles does this jar contain ?
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Let number of white marbles in the jar = $x$
$\therefore P(\text{white marbles}) = \frac{x}{54}$ (1 Mark)
$P(\text{white}) = 1 - \frac{1}{3} - \frac{4}{9} = \frac{9-3-4}{9} = \frac{2}{9}$ (1 Mark)
$\frac{x}{54} = \frac{2}{9}$
$x = 12$ (1 Mark)
Hence, the number of white marbles = $12$
$\therefore P(\text{white marbles}) = \frac{x}{54}$ (1 Mark)
$P(\text{white}) = 1 - \frac{1}{3} - \frac{4}{9} = \frac{9-3-4}{9} = \frac{2}{9}$ (1 Mark)
$\frac{x}{54} = \frac{2}{9}$
$x = 12$ (1 Mark)
Hence, the number of white marbles = $12$