A jar contains 5 red marbles, 4 blue marbles, and 3 green marbles. Two marbles are drawn at random without replacement. What is the probability that the two marbles are of the same color?
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Correct answer
A. 19/66
Principle or equation
For drawing without replacement, the probability of an event is the number of favorable outcomes divided by the total number of equally likely outcomes. The total number of ways to draw 2 marbles from 12 is C(12,2). The favorable outcomes are drawing 2 red, 2 blue, or 2 green.
Why this answer is correct
Total marbles = 5+4+3 = 12. Total ways to choose 2 = C(12,2) = 66. Ways to choose 2 red = C(5,2)=10; 2 blue = C(4,2)=6; 2 green = C(3,2)=3. Favorable = 10+6+3=19. Probability = 19/66.
Example
If a bag has 3 red and 2 blue, the probability of drawing two red without replacement is C(3,2)/C(5,2)=3/10.
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