Question:
A box contains 5 pink, 3 green, and 2 yellow balls. Three balls are picked up randomly. What is the probability that none of the balls drawn is green?
A box contains 5 pink, 3 green, and 2 yellow balls. Three balls are picked up randomly. What is the probability that none of the balls drawn is green?
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Treat "not green" as a single group of 7 balls to simplify the calculation.
Updated On: May 13, 2026
- 3/16
- 7/24
- 5/13
- 4/23
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
Probability = (Favorable outcomes) (Total outcomes).
Step 2: Meaning
Total balls = $5 + 3 + 2 = 10$. Total ways to pick 3 balls = $^{10}C_3$.
Step 3: Analysis
"None is green" means picking 3 balls from the 7 non-green balls (5 pink + 2 yellow). Favorable ways = $^7C_3$.
Probability = $^7C_3 / ^{10}C_3 = [ (7 \times 6 \times 5) / (3 \times 2 \times 1) ] / [ (10 \times 9 \times 8) / (3 \times 2 \times 1) ] = 35 / 120$.
Step 4: Conclusion
Simplifying $35/120$ by dividing by 5 gives $7/24$. Final Answer: (B)
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