Question

Consider two events such that P(A) = 1/4 , P(B) = 2/3 , and P(A ∩ B) = 1/5 . Are events A and B independent events?

Yes, they are independent because P(A) ⋅ P(B) = P(A ∩ B)
No, they are dependent because P(A) ⋅ P(B) = P(A ∩ B)
Yes, they are independent because P(A) ⋅ P(B) ≠ P(A ∩ B)
No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)

Answer 1

p(A) = 1/4
p(B) = 2/3
p(A ∩ B) = 1/5
p(A).p(B) = 2/12 = 1/6 ≠p(A ∩ B )
thus no, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)