alleryIf the probability that a student passes a CAT mock test is $0.6$, what is the probability that the student FAILS?
A$0.6$
B$0.4$
C$0.3$
D$0.5$
Answer & Solution
Correct answer: B. $0.4$
1. 'Pass' and 'fail' are COMPLEMENTARY events: they are mutually exclusive AND exhaustive.
2. By the complement rule: $P(\text{fail}) = 1 - P(\text{pass})$.
3. Plug in: $P(\text{fail}) = 1 - 0.6 = 0.4$.
4. Sum check: $P(\text{pass}) + P(\text{fail}) = 0.6 + 0.4 = 1.0$ ✓ (since they cover all possibilities).
5. Option A would repeat $P(\text{pass})$. Options C, D are arithmetic errors.
_Source: syllabus Mathematics, Ch 14, §14.2.2 (Complement of an event), p. 8–9._
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