Question
A box contains red, green, and blue balls. The
probability of picking a blue ball at random is 1/4. The combined number of red and green balls is 15. If the number of green balls is 3 more than the number of blue balls, what is the probability of picking 2 red and 1 green ball?Solution
ATQ,
Probability of picking red and green balls = 1 – 1/4 = 3/4 Let total number of balls = 4x and red + green = 3x So, 3x = 15 ⇒ x = 5 Total number of balls = 4x = 20 Number of blue balls = x = 5 Number of green balls = 5 + 3 = 8 Number of red balls = 15 – 8 = 7 Required probability = (⁷C₂ × ⁸C₁) / ²⁰C₃ = 14/95
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