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If I have 3 red marbles and 7 blue marbles and pick and replace marbles with like marbles, what is the probability of picking 3 red marbles in a row?
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\[\Big\lgroup\frac{Num_Red}{Total_Marbles}\Big\rgroup*\Big\lgroup\frac{Num_Red}{Total_Marbles}\Big\rgroup*\Big\lgroup\frac{Num_Red}{Total_Marbles}\Big\rgroup\]
Imagine this as 3 independent trials using 3 bags of marbles in a row. Each bag has 3 of 10 marbles that are red. The result of one bag is independent of the result of the other bags -- so there is the same fraction, multiplied 3 times for the three seperate bags.
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