Question

What statements are correct? Check all that apply.

The conditional probability formula is P(X │ Y) = StartFraction P (X intersection Y) Over P (Y) EndFraction.
The conditional probabilities P(D │ N) and P(N │ D) are equal for any events D and N.
The notation P(R │ S) indicates the probability of event R, given that event S has already occurred.
Conditional probability applies only to independent events.
Conditional probabilities can be calculated using a Venn diagram.

Answer 1

Correct statements: 1, 3, and 5.

Brief notes:
- 1 is the definition: P(X|Y) = P(X ∩ Y) / P(Y), provided P(Y) > 0.
- 3 correctly describes the meaning of P(R|S) (again implicitly P(S) > 0).
- 5 is true: Venn diagrams can be used to compute conditional probabilities by comparing the area (or probability) of the intersection to that of the conditioning event.

Statements 2 and 4 are false. 2 is not generally true (P(D|N) ≠ P(N|D) in general). 4 is false because conditional probability applies to dependent or independent events (independence is a special case where P(A|B)=P(A)).