A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability of drawing a red or blue marble?

Question

Accepted Answer

4/5. The total number of marbles is 5 + 3 + 2 = 10. The number of red or blue marbles is 5 + 3 = 8. Since the events "red" and "blue" are mutually exclusive (a marble cannot be both red and blue), the probability of drawing a red or blue marble is P(red or blue) = P(red) + P(blue) = 5/10 + 3/10 = 8/10 = 4/5.

Note that "8/10" and "4/5" represent the same value, but 4/5 is the simplified (reduced) form. On the CLEP exam, answers are typically presented in simplified form. To simplify 8/10, divide both numerator and denominator by their GCD, which is 2: 8/10 = 4/5. "1/2" (1/2 = 5/10) would be the probability of drawing only a red marble. "3/5" (3/5 = 6/10) does not correspond to any correct calculation in this problem.

For mutually exclusive events (events that cannot occur simultaneously), the addition rule simplifies to P(A or B) = P(A) + P(B). If events are NOT mutually exclusive (they can occur together), we must use the general addition rule: P(A or B) = P(A) + P(B) - P(A and B) to avoid double-counting the overlap. In this marble problem, a single marble has only one color, so the events are mutually exclusive and no subtraction is needed. Understanding when to add probabilities and when to subtract the overlap is a key skill for the CLEP exam.

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