A jar contains 5 red marbles, 3 blue marbles, and 2 green marbles. Two marbles are drawn at random without replacement. What is the probability that the two marbles are of different colors?
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Correct answer
A. 31/45
Principle or equation
For drawing without replacement, use combinations to count favorable outcomes. The probability of different colors is 1 minus the probability of same color, or directly sum the probabilities of each pair of different colors.
Why this answer is correct
Total marbles = 10. Total ways to draw 2: C(10,2) = 45. Favorable outcomes: one red and one blue: 5*3 = 15; one red and one green: 5*2 = 10; one blue and one green: 3*2 = 6. Sum = 31. Probability = 31/45.
Example
If a bag has 4 red and 6 blue, drawing 2 without replacement, probability of different colors = (4*6)/C(10,2) = 24/45 = 8/15.
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