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Probability of typing a wrong Bitcoin address

How likely is it that a mistyped Bitcoin address is a valid address? How likely is it that some address is a plausible typo of another?

I heard someone say that Bitcoin is dangerous because you could easily make a typo when entering an address, sending money to the wrong person, and have no recourse. There are dangers associated with Bitcoin, such as losing a private key, but address typos are not a major concern. There’s about a 1 in 10 39 chance that a random 160-bit sequence corresponds to an address somewhere on the Bitcoin blockchain.

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