SOLUTION: A box contains 4 ​red, 2 white and 3 green balls. Two balls are drawn out of the box in succession without replacement. What is the probability that both balls are the same​ co

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Question 1150267: A box contains 4 ​red, 2 white and 3 green balls. Two balls are drawn out of the box in succession without replacement. What is the probability that both balls are the same​ color?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the probability that both balls are the same​ color?
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Both the same color?
As opposed to only one of them being the same color?

Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.


There are 4 + 2 + 3 = 9 balls, in all.


The number of all pairs of balls is  %289%2A8%29%2F2 = 9*4 = 36.  (The order of balls in pairs does not matter).


The number of all pairs consisting of red balls is  %284%2A3%29%2F2 = 6.


The number of all pairs consisting of white balls is 1.


The number of all pairs consisting of green balls is  %283%2A2%29%2F2 = 3.



Thus the desired probability  is  P = %286%2B1%2B3%29%2F36 = 10%2F36 = 5%2F18.    ANSWER

Solved.