Question

Which expression gives Bayes' Theorem for \[P(B_i\mid A)\]?

Options

• \[P(B_i\mid A)=\frac{P(B_i)P(A\mid B_i)}{\sum_{i=1}^{n}P(B_i)P(A\mid B_i)}\]

• \[P(B_i\mid A)=\frac{P(A)}{P(B_i)P(A\mid B_i)}\]

• \[P(B_i\mid A)=P(B_i)+P(A\mid B_i)\]

• \[P(B_i\mid A)=\sum_{i=1}^{n}P(B_i)P(A\mid B_i)\]

Answer 1

Bayes' Theorem divides the joint contribution \[P(B_i)P(A\mid B_i)\] by the total probability of \[A\]. The denominator sums this contribution over all mutually exclusive and exhaustive events.