Independent trials that result in a success with probability p and failure 1 - p are performed. Let $\displaystyle P_n$ denote the probability that n Bernoulli trials result in an even number of successes (0 considered even). Show that

$\displaystyle P_n = p(1-P_{n-1}) + (1-p)(P_{n-1})$

I am not sure what events to condition on to provide this formula. I am fairly stumped!