# A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of randomly selecting a blue marble, then without replacing it, randomly selecting a green marble?

Dec 16, 2016

$\frac{1}{9}$

#### Explanation:

Initial condition:

3 red
2 blue
5 green

Total $3 + 2 + 5 = 10$

Probability of blue is $\frac{2}{10}$
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Second condition:

3 red
1 blue
5 green

New total $3 + 1 + 5 = 9$

Probability of green is $\frac{5}{9}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Total probability of selecting this path is:

$\frac{2}{10} \times \frac{5}{9} \text{ "=" "2/9xx5/10" "=" "2/9xx1/2" "=" } \frac{1}{9}$