Suppose E and F are mutually exclusive events and P(E∪F) ≠ 0. What is P(E|E∪F)?
B) 1
C) 0

Question

Suppose E and F are mutually exclusive events and P(E∪F) ≠ 0. What is P(E|E∪F)? ​
B) 1 
C) 0

Quizplus · Accepted Answer

P(E|E∪F) = P(E∩(E∪F))/P(E∪F)
Since E and F are mutually exclusive, E∩F = ∅.
So, E∩(E∪F) = E.
Therefore, P(E|E∪F) = P(E)/P(E∪F)
Since P(E∩F) = ∅, P(E∪F) = P(E) + P(F).
Since P(E∪F) ≠ 0, P(E) ≠ 0 and P(F) ≠ 0.
Since E and F are mutually exclusive, P(E∩F) = ∅, which means P(E) + P(F) = P(E) + 0 or P(E) + P(F) = 0 + P(F). In either case, P(E∪F) = P(E) + P(F) = P(E) + 0 or P(E) + P(F) = 0 + P(F) = P(F).
Thus, P(E∪F) = P(E) + P(F) = P(E) or P(E∪F) = P(F).
So, P(E|E∪F) = P(E)/P(E∪F) = P(E)/P(E) = 1.

Suppose E and F Are Mutually Exclusive Events and P(E∪F)