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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
avatar+88899 
+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

 

 

cool cool cool

CPhill  Aug 13, 2018
 #2
avatar+199 
+2

You are the best! Thanks! When I signed up I thought the fast respond times were faked, but they are real and awesome!!!smiley

ColdplayMX  Aug 13, 2018
 #3
avatar+88899 
+2

Thanks...I try to give correct answers, but I don't promise anything !!!

 

 

cool cool cool

CPhill  Aug 14, 2018

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