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# Probability Question check

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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
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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 [ At least we got the same answer  !!! ]   Sep 15, 2019
edited by CPhill  Sep 15, 2019
edited by CPhill  Sep 15, 2019
#2
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Thanks CPhill, that is a simpler method!

Sep 15, 2019