Let A and B be two events in a probability space with P(A) = 0.3, P(B) = 0.5, and P(A B) = 0.1. Which of the following statements is/are TRUE?

P(A B^c) = 0.2, where B^c is the complement of the event B

The two events A and B are independent

P(A B^c) = 0.2, where B^c is the complement of the event B

P(A^c B^c) = 0.4, where A^c and B^c are the complements of the events A and B, respectively

GATE CSE 2024 Session 1 Q27: Independence and union/intersection probabilities of A and B

Engineering Mathematics
1 mark
MSQ
No negative marking

Let $A$ and $B$ be two events in a probability space with $P(A) = 0.3$ , $P(B) = 0.5$ , and $P(A \cap B) = 0.1$ . Which of the following statements is/are TRUE?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: B, C (official GATE 2024 final answer key)

Concept used: Inclusion–exclusion and De Morgan's law for events.

First step: Compare $P(A)P(B) = 0.15$ with $0.1$ , then compute $P(A \cup B) = 0.3 + 0.5 - 0.1$ .

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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GATE CSE 2024 Session 1 Q27: Independence and union/intersection probabilities of A and B

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