You are misunderstanding how to use probability with multiple attempts. It's not the individual attempt probablility that is in question. It's the cumulative probablility.

Example: Coin flipping. Pretend Heads = Getting Mount. Tails = Not getting Mount. What is more likely to happen?

A) Getting a Heads in 1 flip

B) Getting a Heads in 5 flips

From your description, the chance of both A and B happening are exactly the same since each indidivudal attempt is a 50% chance.

Well, let's prove what really happens. Try flipping a coin until you get Heads. Repeat that 5000 times. You will see that A happens much less than B. This will happen every single time you do it.

Now, for clarification, this is not a linear relationship. There will never be a 100% chance of getting Heads or Tails. But your chance of "not getting Heads" 100x in a row is low.