In a box there are 5 red, 3 blue, and 2 green balls. Two balls are drawn without replacement. Find the probability that both balls are of different colors.
Answer
31/45
The correct answer is 31/45 — Probability = favourable / total = 31/45.
Step-by-step solution
- Total balls = 5+3+2 =10.
- Number of ways to choose 2 balls without replacement = C(10,2)=45.
- Count favourable ways where two balls are different colors. Case 1: Red & Blue: C(5,1)*C(3,1)=15. Case 2: Red & Green: 5*2=10. Case 3: Blue & Green: 3*2=6. Total favourable =15+10+6=31.
- Probability = favourable / total = 31/45.
Common mistake: Treating draws as independent or miscounting same color pairs
Concept tested: Compound probability without replacement
Published · How this solution was prepared and checked
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