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Yes. You can still try to get it in one attempt.

Odds in one attempt: 1 in 32

Odds in two attempts: 1 in 1

Your odds add up to more than 1.

Probabilities sum to 1.0. Odds don't sum.

Odds of getting it within 2 attempts is 1. Odds of getting it on exactly the second attempt is 31/32

Ooops:

You won!

You guessed 01111 in 4 attempts!

Well yeah and a fair coin has P(heads) == P(tails) == 0 for someone who eats it.