Let 𝐴 and 𝐵 be two events in a probability space with 𝑃(𝐴) = 0.3, 𝑃(𝐵) =…

GATE · 2024 · CS · Set 1 · Computer Science & IT

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?

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

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