Probability question

dzim

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Joined
Mar 19, 2019
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2
I'm having trouble helping my daughter on this question.
"In Box A there are 3 black and 5 green marbles. In Box B there are 4 black marbles and 6 green marbles. One marble is taken from each box. What is the probability that both marbles are the same colour?" The answer in the textbook is 21/40 but we are not sure how to get that. Any help would be appreciated.
 

MarkFL

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Nov 24, 2012
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Hello, and welcome to FMH! :)

I would first look at the probability that both marbles are black...we'll call this event B:

\(\displaystyle P(B)=\frac{3}{8}\cdot\frac{4}{10}=\frac{3}{20}\)

Next, let's look at the probability that both marbles are green...we'll call this event G:

\(\displaystyle P(G)=\frac{5}{8}\cdot\frac{6}{10}=\frac{3}{8}\)

Now, if event X is that both marbles are the same color, then:

\(\displaystyle P(X)=P(B\text{ OR }G)=\frac{3}{20}+\frac{3}{8}=\frac{21}{40}\)

Does that make sense?
 

dzim

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Mar 19, 2019
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2
sure does. Thanks
 
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