Question

If A and B are two events such that A ⊂ B and P (B) ≠ 0, then which of the following is correct?

Options

• P(A|B) = `(P(B))/(P(A))`

• P(A|B) < P(A)

• P(A|B) ≥ P(A)

• None of these

Answer 1

P(A|B) ≥ P(A)

Explanation:

A ⊂ B ⇒ A ∩ B = A and P(B) ≠ 0

P(A|B) = `(P(A ∩ B))/(P(B))`

= `(P(A))/(P(B))`

P(B) ≠ 0, 

∴ `(P(A))/(P(B)) < 1`

⇒ P(A) < (P(B) 

∴ P(A|B) ≥ P(A)