1. Let E and F are two events of a sample space S, then
2. If A and B are two events of a sample S and F is another event such that P(F) ≠ 0, then
P[(A ∪ B)/F] = P(A/F) + P(B/F) - P[(A ∩ B)/F]
Specially, if A and B are two mutually exclusive events then
P[(A ∪ B)/F] = P(A/F) + P(B/F) - P[A ∩ B)/F]
Specially, if A and B are two mutually exclusive events then
P[(A ∪ B)/F] = P(A/F) + P(B/F)
We know that
When A and B are mutually exclusive,
P[(A ∩ B)/F] = 0
⇒ P[(A ∪ B)/F] = P(A/F) + P(B/F)
Thus, when A and B are mutually events, then
3. P(E'/F) = 1 - P(E/F)
We know that
P(S/F) = 1
⇒ P[E ∪ F)/F] = 1 [∵ S = E ∪ F]
⇒ P(E/F) + P(E'/F) = 1 [∵ E and F are mutuallly exclusive events]
Thus, P(E'/F) = 1 - P(E/F)
