A bag contains 15 red and 20 black balls. Each ball is numbered 1, 2 or 3. 20% of red balls are numbered 1 and 40% are numbered 3. Similarly 45% of black balls are numberd 2 and 30% are numbered 3. One ball is drawn at random and found to be numbered 2. If probability that it was red ball is p, then 15p is

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Detailed Solution

(1)         (2)       (3 )
Red balls 20%     40%     40%
Black balls 25%     45%     30%

$P = \frac{\frac{15}{35} \times \frac{40}{100}}{\frac{15}{35} \cdot \frac{40}{100} + \frac{20}{35} \times \frac{45}{100}}$
$P = \frac{40}{40 + 60} = \frac{2}{5}$

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