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The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\frac{12}{23}$, find the total number of balls in the given bag.
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Let number of black balls = $x$, then number of red balls = $x+3$. $\therefore$ total number of balls = $2x+3$ ($\frac{1}{2}$ mark). ATQ, $\frac{x+3}{2x+3} = \frac{12}{23}$ ($\frac{1}{2}$ mark). $x = 33$ ($\frac{1}{2}$ mark). Total number of balls = 69 ($\frac{1}{2}$ mark).