If an event has a 10% chance of happening, why is it not guaranteed to happen in 10 tries?
Because with every new try, the chance starts all over again. You cannot ACCUMULATE chances. But when you make for example 1000 'throws' you'll see a more equal pattern occur.
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.)
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