Ravi has a bag full of 10 Nestle and 5 Cadbury chocolates. Out of these, he…
2025
Ravi has a bag full of 10 Nestle and 5 Cadbury chocolates. Out of these, he draws two chocolates. What is the probability that he would get at least one Nestle chocolate?
- A.
19/21
- B.
3/7
- C.
2/21
- D.
1/3
Show answer & explanation
Correct answer: A
Concept: For ‘at least one’ probability questions, use direct counting or the complement rule: P(at least one favourable) = 1 − P(none favourable). Count selections using combinations (nCr = ways to choose r items from n, order not mattering), then divide by the total ways to draw 2 chocolates from the bag.
Total chocolates = 10 Nestle + 5 Cadbury = 15. Total ways to draw 2 chocolates = 15C2 = (15 × 14)/2 = 105.
Ways to get at least one Nestle = (ways to pick exactly 1 Nestle and 1 Cadbury) + (ways to pick 2 Nestle) = (10C1 × 5C1) + 10C2 = (10 × 5) + 45 = 50 + 45 = 95.
Required probability = 95/105 = 19/21.
Cross-check: By the complement rule, P(no Nestle) = P(both Cadbury) = 5C2/15C2 = 10/105 = 2/21. So P(at least one Nestle) = 1 − 2/21 = 19/21 — the same result.
Hence, the required probability of drawing at least one Nestle chocolate is 19/21.