The most common form splits on an event and its complement, which together always form a partition:

$$P(A) = P(A \mid B)P(B) + P(A \mid B^c)\bigl(1 - P(B)\bigr)$$

Return $P(A)$.

solve(0.95, 0.05, 0.01)  ->  0.059
# A test with 95% sensitivity and a 5% false-positive rate, disease prevalence 1%.
# This is the denominator Bayes' theorem needs.