Mathematics

Problem

Which one of the following correctly expresses the probability of an event

A

in terms of a partition

\{E_1,E_2,\dots ,E_n\}

of the sample space with

P(E_i)>0

for every

i

? a)

\displaystyle P(A)=\sum_{i=1}^{n}P(A)\,P(E_i\mid A)

\displaystyle P(A)=\sum_{i=1}^{n}P(A\mid E_i)

\displaystyle P(A)=\sum_{i=1}^{n}P(E_i)\,P(A\mid E_i)

\displaystyle P(A)=\sum_{i=1}^{n}\bigl[P(E_i)+P(A\mid E_i)\bigr]