An urn contains 6 yellow balls and x black balls. When two balls are drawn at random, the probability that both are yellow is 5 26 , then the value of x is

Step-by-step solution

Let Y = 6 be the number of yellow balls and X = x be the number of black balls, so the total number of balls is N = 6 + x . The probability of drawing two yellow balls is the ratio of combinations: 6 2 6 + x 2 = 5 26 . Evaluating the combinations, 6 2 = 15 and 6 + x 2 = (6 + x)(5 + x) 2 , so: 15 (6 + x)(5 + x) 2 = 5 26 . Simplifying, 30 (6 + x)(5 + x) = 5 26 . Dividing both sides by 5: 6 (6 + x)(5 + x) = 1 26 . Cross-multiplying: (6 + x)(5 + x) = 156 . Solving, x^2 + 11x + 30 = 156 and then x^2 + 11x - 126 = 0 . Fa