Bayes' Theorem provides the probability of a cause given an observed event: $P(E_i|A) = \frac{P(E_i)P(A|E_i)}{\sum_{j=1}^n P(E_j)P(A|E_j)}$.
The Partition Rule
Always verify that events $E_1, E_2, \dots, E_n$ form a mutually exclusive and exhaustive partition of the sample space: $\sum P(E_i) = 1$. Clearly state the definition of event $A$ (the common observed event) at the top of your solution.