Question
A box contains (x + 3) black balls, 6 yellow balls, and
5 orange balls. If two balls are selected at random and the probability of selecting two orange balls is 10/153, what is the difference between the number of black balls and orange balls?Solution
5C2 / (x + 14) C2= 10/153 [(5 * 4) / (1 * 2)] / [(x + 14) (x + 13) / (1 * 2)] = 10/153 (2 * 153) = x2 + 14x + 13x + 182 306 = x2 + 27x + 182 x2 + 27x - 124 = 0 x2 + 31x – 4x – 124 = 0 X(x + 31) – 4(x + 31) = 0 (x – 4) (x + 31) = 0 x = 4, -31 (negative value will be eliminated) Required difference = 7 – 5 = 2 balls
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