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Experimental/Empirical Probability

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Question

There are 20 red balls and 15 green balls in a box. If some red balls are to be subtracted from the box so that the probability of randomly drawing a red ball becomes $\frac{2}{5}$ , then how many red balls must be subtracted from the box ?

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Solution

Let x be the number of red balls to be subtracted.
According to the question,
$\frac{20 - x}{35 - x} = \frac{2}{5}$

$5 (20 - x) = 2 (35 - x)$
$100 - 5 x = 70 - 2 x$
$x = 10$

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