Buildreps has already given an easy and succinct explanation, so I'll try to give a mathematical proof. Do correct me if I'm wrong anywhere.
Suppose the chance of event A happening is 10% for a given attempt; the chance of it not happening for the same attempt is then 90%. (We assume there are only two outcomes: event A happens, or it doesn't happen.)
For 10 tries, the probability of event A not happening AT ALL is 0.9^10 (0.9 to the power of 10), which is about 0.3487. Therefore, the probability of event A happening AT LEAST ONCE within 10 tries is 1-0.3487 = 0.6513. You can see that the probability of A happening at least once is not 1, showing that it's not guaranteed that A will actually happen at all within ten tries (although the probability is high.)