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A bag contains 4 red marbles and 5 blue marbles. Two marbles are randomly drawn without replacement.

Find the probability both marbles are red.

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Arkady E. | Math PhD Student and College InstructorMath PhD Student and College Instructor
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Number the red marbles 1-4 and the blue marbles 5-9. Then there are 4 possibilities for drawing the first red marble and 3 possibilities for drawing the second red marble. On the other hand, there are 9 choices for the first marble and 8 choices for the second marble.
 
Hence the desired probability is 4x3/9x8  = 1/6