+210 A bag contains ten balls, some of which are red and the rest of which are yellow. When two balls are drawn at random at the same time, the probability that both balls are red is \(\frac{1}{15}\). How many balls in the bag are red?
+128460 Let the number of red balls = x
So we have that
[x / 10] * [ (x - 1) / 9 ] = 1/15 simplify
x(x - 1) / 90 = 1/15 multiply both sides by 90
x ( x - 1) = 6
x^2 - x - 6 = 0 factor
(x -3) ( x + 2) = 0 set each facotr to 0 and solve for x and we get that
x = 3 or x = -2 reject the second answer
So...there are 3 red balls
Proof : First Draw Probability of Red * Second Draw Probability of Red =
3 / 10 * 2 / 9 = 6 / 90 = 1 / 15
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