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A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we know that the first toss is a head than if we know that at least one of the tosses is a head.

This is an excerpt from Introduction of Probability SECOND EDITION. Is this correct usage? I thought we should use "as adj. as"

Regardless of the correctness of the above passage, how is my rewrite below? Does it contain grammatical errors?

Alice claims that the event of two heads if we know that the first toss is a head is as likely as if we know that at least one of the tosses is a head.

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You are right to change the than to an as, but you can't just change at least as likely to as likely. They don't mean the same thing. Also, the change in sentence structure has rendered it less readable, if not ungrammatical (I'm having enough trouble parsing it that I'm not sure). Commas might help, or might make it even more awkward.

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The original sentence has a number of problems, one of which you've correctly identified.

"The event...is at least as likely if [A] than if [B]" is not correct. A correct phrasing would compare the likelihoods with as: "The outcome is as likely in case A as it is in case B."

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