Question 1135955
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Answer in fraction form: <font color=red>19/66</font>
Answer in decimal form: <font color=red>0.2879</font> (this value is approximate)


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Work Shown:


Define the three events
R = event of getting red
B = event of getting blue
G = event of getting green


For any single marble, we have these three probabilities
P(R) = 4/12 since there are 4 red out of 12 total
P(B) = 3/12 since there are 3 blue out of 12 total
P(G) = 5/12 since there are 5 green out of 12 total


Let's compute the probabilities for getting two of the same color, for any given color R, G or B
P(RR) = probability of getting two red in a row
P(RR) = (4/12)*(3/11) = 12/132 
P(BB) = probability of getting two blue in a row
P(BB) = (3/12)*(2/11) = 6/132
P(GG) = probability of getting two green in a row
P(GG) = (5/12)*(4/11) = 20/132
The values step down because we do not replace the marble we selected.


Note how I did not reduce the fractions. This was to ensure the denominators stays the same, so we can then add the fractions as such
P(RR or BB or GG) = P(RR) + P(BB) + P(GG)
P(RR or BB or GG) = 12/132 + 6/132 + 20/132
P(RR or BB or GG) = (12 + 6 + 20)/132
P(RR or BB or GG) = 38/132
Extra info: the addition formula used is only possible because the events RR, BB and GG are mutually exclusive. For example, it is impossible for the events RR and BB to happen simultaneously. This is assuming we only select two marbles.


Now reduce the fraction as much as possible. We do so by dividing both parts (38 and 132) by the GCF 2
38/2 = 19
132/2 = 66


So 38/132 reduces to <font color=red>19/66</font> which is roughly equivalent to <font color=red>0.2879</font> (rounded to four decimal places)
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