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?

ColdplayMX
Aug 13, 2018

#1**+2 **

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

CPhill
Aug 13, 2018

#2**+2 **

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ColdplayMX
Aug 13, 2018