Question
A bag contains only red and blue balls. The probability
of drawing a red ball from the bag is 3/5. If 4 more blue balls are added to the bag, the probability of drawing a red ball becomes 1/2. Find the original number of red and blue balls in the bag.Solution
Let original red = R, blue = B. P(red) initially: R/(R + B) = 3/5 ⇒ 5R = 3(R + B) 5R = 3R + 3B 2R = 3B R = 1.5B. ...(i) After adding 4 blue, red = R, blue = B + 4, total = R + B + 4. New probability: R/(R + B + 4) = 1/2 ⇒ 2R = R + B + 4 ⇒ R = B + 4. ...(ii) From (i): R = 1.5B. So 1.5B = B + 4 0.5B = 4 B = 8. Then R = B + 4 = 12. Answer: Originally 12 red and 8 blue balls.
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