GATE CSE 2024 | Set 1 | Question: 17

Question

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?

• A. The two events $A$ and $B$ are independent
• B. $P(A \cup B)=0.7$
• C. $P\left(A \cap B^c\right)=0.2$, where $B^c$ is the complement of the event $B$ 
• D. $P\left(A^c \cap B^c\right)=0.4$, where $A^c$ and $B^c$ are the complements of the events $A$ and $B$, respectively 

Answer 1

P(A u B) = 0.7, Option B is correct

P(A)*P(B) = 0.15, Option A is incorrect as for independent events P(A n B) = P(A)*P(B)

For C, it will be equal to P(A) - P(A n B) = 0.3 - 0.1 = 0.2, So C is correct

For D, it is 1 - P(AuB) = 1 - 0.7 = 0.3, So D is incorrect.

Answers: B,C