Well, from venn diagram it looks pretty obvious that the
P(A) = P1 + P2
But, I tried another approach...
@Arjun sir, can you please check this out..
P(A) = P(A/B) + P(A/B')
That is, the probability of occurrence of A is the sum of:
i) Probability that A occurs given that B has occurred: P(A/B)
ii) Probability that A occurs given that B' has occurred: P(A/B')
Since, B and B' totally make up sample space, the occurrence of A is also covered.
P(A/B) = P(A∩B) = P2
P(A/B') = P(A∩B') = P3
P(A) = P2 + P3