Very basic probability problem Firstly, apologies if this question is too trivial or just plain inappropriate for this site...
I want to catch a ball. I have exactly two chances to catch the ball. The ball is thrown in such a way that my chance of catching the ball on the first throw is $55\%$. The next time, the ball is thrown faster, so my chance of catching that throw is only $25\%$.
I only need to catch the ball once. Before the first ball is thrown, what's my overall chance of success?
(My assumption is that this is a simple average (so $40\%$), but I wonder if I'm making a mistake.)

The probability of catching the ball on the first throw is $0.55$, the probability of catching the ball on the second throw is $0.45\cdot0.25$ (the ball wasn't caught on the first throw, but it was caught on the second throw). So the probability of catching the ball is then equal to
$$
0.55+0.45\cdot0.25=0.6625.
$$
