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Does the author have something backwards or do I?

P(RateOfSuccess|Successes) = Beta(α,β)

"In Bayesian terms, C3PO's estimate of the true rate of success given observed data is referred to as the likelihood."

BUT we know likelihood(rateofsuccess|data) = probability(data|rate of success).

I am confused.

"Likelihood" can refer to both p(param|data) and p(data|param). See [1] for an example of the first, and [2] for the second.