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avatar+2390 

A bag contains 5 blue marbles, 4 white marbles, and 3 red marbles. If three marbles are randomly selected from the bag, what is the probability that the marbles selected will be of the same color? Express your answer as a common fraction.

In the future I will need a lot of your guy's help to check my answers, as the math competitions are starting soon! and i need to prepare

 

Also the confirming if I am a robot thing is SUPER annoying. Make it where once you passed the test ONCE, you don't need to do it again if you have an account.

 

How I did it:
 

5 + 4 + 3 = 12 total number of marbles

 

that means 12 choose 3 = 220 ways to choose 3 marbles

 

Now the question asks how many ways will the marbles be the same color

 

So for red

 

there is only 1 way

 

For White,

 

there is 4 ways of choosing 3 out of 4

 

And for blue 

 

there is 10 ways of choosing 3 out of 5

 

So is 1 + 4 + 10 = 15 ways you can pick three marbles of the same color

 

So 15/220 = 3/44

 Sep 15, 2019
edited by CalculatorUser  Sep 15, 2019
edited by CalculatorUser  Sep 15, 2019
edited by CalculatorUser  Sep 15, 2019
 #1
avatar+104911 
+2

Not great at probability, but we could either draw 3 red marbles, 3 blue marbles or 3 white marbles

 

P(red)   = (3/12) (2/11) (1/10)  =  6 / 1320

 

P( blue)  = (5/12) (4/11) (3/10)  = 60/1320

 

P(white) = (4/12) (3/11)(2/10)  = 24 / 1320

 

So.....the total probability =  [ 6 + 60 + 24 ] /1320   =  90 / 1320  =  9 /132   =   3 / 44

 

Good job, CU   smiley    [ At least we got the same answer  !!! ]

 

 

cool cool cool

 Sep 15, 2019
edited by CPhill  Sep 15, 2019
edited by CPhill  Sep 15, 2019
 #2
avatar+2390 
+2

Thanks CPhill, that is a simpler method!

 Sep 15, 2019

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