Select independent or not independent for each description of events. p(a)=0.3, p(b)=0.5, p(a|b)=0.15 p(a)=0.2, p(b)=0.4, p(a|b)=0.2 p(a)=0.6, p(b)=0.2, p(a|b)=0.3

When two events X and Y are independent,

Then, P(X ∩ Y) = P(X) × P(Y)

We know that,

Thus, by substituting the value of P(X ∩ Y),

Which is the required condition for independent events.

In first option,

P(A)=0.3, P(B)=0.5, P(A|B)=0.15

⇒ A and B are not independent events

In second option,

P(A)=0.2, P(B)=0.4, P(A|B)=0.2

⇒ A and B are independent events.

In third option,

P(A)=0.6, P(B)=0.2, P(A|B)=0.3

⇒ A and B are not independent events

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