Question
A vessel contains 5 red, ‘x’ green and 3 blue
ribbons. If two ribbons are drawn from the vessel randomly, then the probability of getting a red and a green ribbon is 3/11. Find the value of x.Solution
Total number of ribbons = (x + 8) According to question; (xC1 × 5C1)/(x + 8)C2 = 3/11 2 × 5x/(x + 8)(x + 7) = 3/11 110x = 3 × (x2 + 15x + 56) 110x = 3x2 + 45x + 168 3x2 – 65x + 168 = 0 3x2 – 9x – 56x + 168 = 0 3x(x – 3) – 56(x – 3) = 0 (3x – 56)(x – 3) = 0 So, x = 56/3 or x = 3 Since number of ribbons can’t be in fraction Therefore, x = 3
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