A bag contains 12 balls that are indistinguishable by touch, 5 of which are red. Two balls are drawn without replacement. What is the probability that no red ball is drawn?
A) 49/144
B) 7/22
C) 15/22
D) 25/132
E) 49/132
IMAT 2026 · Question 58
Q58 - Probability
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The correct answer is B) 7/22.
There are 12 − 5 = 7 non-red balls. Draw twice without replacement, so the second draw has one ball less of each kind:
First ball not red: 7/12
Second ball not red: 6/11
P = 7/12 × 6/11 = 42/132 = 7/22
Same result with combinations: C(7,2) / C(12,2) = 21/66 = 7/22.
Traps: 49/144 (A) is the answer with replacement (7/12 × 7/12); 15/22 (C) is the probability of drawing at least one red ball (1 − 7/22).
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