Is my Venn diagram for probability of event B correct?

[tzx9633]

Homework Statement

It's given that the total probability of event b =P(B)

If A1 , A2 ... An are mutually exclusive and exhaustive events , then probability of B =

Homework Equations

The Attempt at a Solution

P(B) = P(A1) x P(B | A1) + P(A2) x P(B | A2) + P(A3) x P(B | A3) + ... P(An) x P(B | An)

IS it correct if i represent them in this Venn's diagram ?

 

[Orodruin]

IS it correct if i represent them in this Venn's diagram ?

That depends. Is the region not included in any of the blue circles one of the Ai?

 

[Ray Vickson]

Homework Statement

It's given that the total probability of event b =P(B)

If A1 , A2 ... An are mutually exclusive and exhaustive events , then probability of B =

Homework Equations

The Attempt at a Solution

P(B) = P(A1) x P(B | A1) + P(A2) x P(B | A2) + P(A3) x P(B | A3) + ... P(An) x P(B | An)

IS it correct if i represent them in this Venn's diagram ?

The statement $P(B) = \sum_{i=1}^n P(A_i) P(B|A_i)$ is correct ONLY if $B \subset \cup_{i=1}^n A_i$. In your case you said the $\{ A_i \}$ are mutually exclusive and exhaustive (meaning that $\cup_{i=1}^n A_i$ is the whole sample space), so the equation is correct. I guess you are asking if your Venn diagram is also correct. Well, do you have $B \subset \cup_{i=1}^n A_i$ in your diagram?