I can't figure out which rules of probability to apply to solve for my probability of the second event. My information for the question is as follows:
$P(A) = 0.3, P(A \cap B) = 0.1$, $P(A\cup B) \setminus (A \cap B) = 0.75$
I need to find the probability of B. Any guidance is appreciated
You have been given $\mathsf P(A), \mathsf P(A\cap B),$ and $\mathsf P((A\cup B)\smallsetminus(A\cap B))$, and wish to evaluate $\mathsf P(B)$ .
Well you can express some of these events as unions of the disjoint events: $(A\cap B), (A\smallsetminus B), (B\smallsetminus A)$. $$\begin{align}A&=(A\cap B)\cup(A\smallsetminus B)\\B &= (A\cap B)\cup(B\smallsetminus A)\\(A\cup B)\smallsetminus(A\cap B)&=(A\smallsetminus B)\cup(B\smallsetminus A)\end{align}$$
So applying the additive rule :
$$\begin{align}\mathsf P(A)&=\mathsf P(A\cap B)+\mathsf P(A\smallsetminus B)\\\mathsf P(B)&=\mathsf P(A\cap B)+\mathsf P(B\smallsetminus A)\\\mathsf P((A\cup B)\smallsetminus(A\cap B))&=\mathsf P(A\smallsetminus B)+\mathsf P(B\smallsetminus A)\end{align}$$