For two events $A$ and $B$, the probability of $A$ can be found using the formula $P(A) = P(A|B)P(B) + P(A|B')*P(B')$ This is simply the weighted average of the conditional probabilities of $A$ given $B$ and $A$ given not $B$ (which will constitute the entire sample space). For the more general case of event $A$ and some number of [[mutually exclusive and collectively exhaustive]] events $B_1 \dots B_k$, the law of total probability can also be written as the sum of the [[joint probability]] of $A$ and each $B_k$. $P(A) = P(B_1 \cap A) + \dots + P(B_k \cap A)$ This form can be expanded in terms of [[conditional probability]] as $P(A) = P(B_1)P(A|B_1) + \dots + P(B_k)P(A|B_k)$ This might seem like an unnecessarily complicated way of calculating the probability of $A$, but we'll see that it comes in handy especially in the field of [[Bayesian statistics]].