A and B are not independent events because of P(A|B) ≠ P(A). Then the correct option is A.
Which pair of events are called independent events?
When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of other events, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent if we have:
[tex]\rm P(A \cap B) = P(A)P(B)[/tex]
Comparing it with the chain rule will give
[tex]\rm P(A|B) = P(A)\\\\P(B|A) = P(B)[/tex]
Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).
A and B are two events.
Let P(A) = 0.6, P(B) = 0.5 and P(A and B) = 0.2 .
Then we have
[tex]\rm P(A|B) = \dfrac{P(A\cap B)}{P(B)}\\\\P(A|B) = \dfrac{0.2}{0.5}\\\\P(A|B) = 0.4 \neq P(A)[/tex]
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