Question

For any three events a,b and c find p(aub /c)

Answer 1

P ((AUB)nC)/P (C)=P ((AnCU (BnC))/P (C)
=P (AnC)/P (C)+P (BnC)/P (C)-P ((AnC)n (BnC))/P (C)
in this question we will use formula P (AUB)=P (A)+P (B)-P (AnB)

Answer 2

Answer:
P((A U B)/C) = P(A/C) + P(B/C) -P((A ∩ B)/C)
Step-by-step explanation:
We know that
P(AUB) = P(A) + P(B) - P(A∩B) ...(1)
And from definition of Conditional Probability,
P(A/B) = P(A∩B)/P(B).......(2)
From (2)
P((A U B)/C) = [P((AUB)∩C)]/P(C) ,
And using distributive property of sets we can see that
((AUB)∩C)= (A∩C)U(B∩C).....(3)
From (1), (2) and (3) it's evident that
P((A U B)/C) = P(A∩C)/P(C) + P(B∩C)/P(C) - P((A∩B)∩C)/P(C),
=> P((A U B)/C) = P(A/C) + P(B/C) -P((A ∩ B)/C).