5. Let A1, A2... A, be arbitrary events, and define C (at least k of the A, occur). Show that

$$\sum_{k=1}^{n} P(C_k) = \sum_{i=1}^{n} P(A_i)$$

HINT: Let X denote the number of the A, that occur. Show that both sides of the above are equal to E[X].