Question

In a bag, there are 10 red, 15 green, and 12 blue marbles. If you draw two marbles (without replacing), what is the approximate probability of drawing two different colors?

• A. 33.33%
• B. 0.06%
• C. None of the other answers
• D. 67.57%
• E. 25%

Hint:

Whenever asked for “different colors”, compute the complement of the probability of “same colors”.

Answer 1

The Correct Option is D

Step 1: Total marbles.
\(10 + 15 + 12 = 37\).

Step 2: Total ways to draw 2 marbles.
\(\binom{37}{2} = \frac{37 \times 36}{2} = 666\).

Step 3: Probability of drawing 2 marbles of same color.
- Red: \(\binom{10}{2} = 45\).
- Green: \(\binom{15}{2} = 105\).
- Blue: \(\binom{12}{2} = 66\).
Total same-color = \(45+105+66 = 216\).

Step 4: Probability of same color.
\(\frac{216}{666} \approx 32.43%\).

Step 5: Probability of different colors.
\(100% - 32.43% = 67.57%\).

Final Answer: \[ \boxed{67.57%} \]