A bag 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, the probability of an event can be computed as the number of favorable combinations divided by the total number of combinations.
Why this answer is correct
Total marbles = 10. Total ways to draw 2 = C(10,2) = 45. Favorable: two different colors. Count all pairs minus same-color pairs. Same-color pairs: C(5,2)+C(3,2)+C(2,2)=10+3+1=14. Favorable = 45 - 14 = 31. Probability = 31/45.
Example
If there are 4 red and 6 blue, probability of different colors = (4*6)/C(10,2)=24/45=8/15.
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