In probability notation, Bayes' theorem is P(A|B) = [P(B|A) P(A)] / P(B). Which term represents the likelihood?

In probability notation, Bayes' theorem is P(A|B) = [P(B|A) P(A)] / P(B). Which term represents the likelihood?

• A. P(A|B)
• B. P(B|A)
• C. P(A)
• D. P(B)

Answer: (B)

In Bayes’ theorem, the likelihood is the probability of the observed data given a specific hypothesis. It’s the part that measures how plausible the data would be if that hypothesis were true. This is written as P(B|A): the probability of seeing the data B under the assumption that A is the actual situation or hypothesis. The other pieces have different roles. P(A) is the prior probability of the hypothesis before seeing any data. P(B) is the overall probability of the observed data under all possible hypotheses (a normalization factor to keep probabilities consistent). P(A|B) is the posterior probability—the plausibility of the hypothesis after observing the data. So the term that represents the likelihood is P(B|A): it links the data you observed to the hypothesis you're testing by telling you how compatible the data are with that hypothesis.

In Bayes’ theorem, the likelihood is the probability of the observed data given a specific hypothesis. It’s the part that measures how plausible the data would be if that hypothesis were true. This is written as P(B|A): the probability of seeing the data B under the assumption that A is the actual situation or hypothesis.

The other pieces have different roles. P(A) is the prior probability of the hypothesis before seeing any data. P(B) is the overall probability of the observed data under all possible hypotheses (a normalization factor to keep probabilities consistent). P(A|B) is the posterior probability—the plausibility of the hypothesis after observing the data.

So the term that represents the likelihood is P(B|A): it links the data you observed to the hypothesis you're testing by telling you how compatible the data are with that hypothesis.