What is the probability of A given A union B? We know that p(A) = 0.5 p(B) = 0.3 p(AB) = 0.1
From my understanding of conditional probability i think it should be p(A)/p(A union B) . Is this correct?
Could I solve this problem using the definition of conditional probability p(A|B) = p(AB)/p(B) and then applying the distributive law.
$\endgroup$ 11 Answer
$\begingroup$You can use the definition of conditional probability, and make use of the absorption law of set theory (highlighted in red below), as follows:- $$P(A|A\cup B)=\frac{P(\color{red}{A\cap(A\cup B)})}{P(A\cup B)}=\frac{P(\color{red}{A})}{P(A\cup B)}$$ So, you are essentially correct.
$\endgroup$ 4
