Stuck on probability question: (A and B are independent) P(B ∩ [not A] | A ∪ B)
I'm having a bit of trouble understanding on how to get from this
(A and B are independent)
P(B ∩ [not A] | A ∪ B)
to this
P(B ∩ [not A]) / P(A ∪ B)
My progress:
P[(B ∩ [not A]) ∩ (A ∪ B)] / P(A ∪ B) =
= P[(B ∩ [not A] ∩ A) ∪ (B ∩ [not A] ∩ B)] / P(A ∪ B) =
= ? (now i'm stuck)
I'm having a bit of trouble understanding on how to get from this
(A and B are independent)
P(B ∩ [not A] | A ∪ B)
to this
P(B ∩ [not A]) / P(A ∪ B)
My progress:
P[(B ∩ [not A]) ∩ (A ∪ B)] / P(A ∪ B) =
= P[(B ∩ [not A] ∩ A) ∪ (B ∩ [not A] ∩ B)] / P(A ∪ B) =
= ? (now i'm stuck)