Question

If p(a|b) = 0.35, p(b) = 0.75 and p(a) = 0.44 are the events a and b independent ?

Answer 1

hello :
note 1 :
p(A|B) = p(A∩B)/ p(B)

note 2 :
A and B independent: p(A∩B) = p(A)×p(B)
calculate : p(A∩B)
p(A∩B) = p(A|B)×p(B)
p(A∩B) = 0.35 ×0.75 = 0.2625
but : p(A)×p(B) = 0.44×0.75 = 0.33
conclusion :
the events A and B are not independent ?