Question

Which formula represents the Law of Total Probability?

Options

• \[P(A)=P(B_i)P(B_i\mid A)\]

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

• \[P(A)=\sum_{i=1}^{n}P(B_i\mid A)\]

• \[P(A)=P(B_i)+P(A\mid B_i)\]

Answer 1

The Law of Total Probability obtains \[P(A)\] by adding the probabilities of \[A\] through every mutually exclusive and exhaustive event \[B_i\]. Each term is \[P(B_i)P(A\mid B_i)\].