Question

Let A and B be two events such that P(A) ≠ 1 and P(B) ≠ 0, then `"P"(bar"B"/bar"A")` = ______.

Options

• `1 - "P"("B"/"A")`

• `1 - "P"(bar"B"/"A")`

• `(1 - "P"("A" ∪ "B"))/("P"(bar"A")`

• `("P"(bar"B"))/("p"(bar"A"))`

Answer 1

Let A and B be two events such that P(A) ≠ 1 and P(B) ≠ 0, then `"P"(bar"B"/bar"A")` = `(1 - "P"("A" ∪ "B"))/("P"(bar"A")`.

Explanation:

`"P"(bar"B"/bar"A") = ("P"(bar"A" ∩ bar"B"))/("P"(bar"A"))`

= `("P"(bar"A ∪ B"))/("P"(bar"A"))`

= `(1 - "P"("A" ∪ "B"))/("P"(bar"A"))`