Is my Venn diagram for probability of event B correct?

In summary, the total probability of event B is equal to the sum of the individual probabilities of event B given each mutually exclusive and exhaustive event A1, A2...An. This can also be represented in a Venn diagram, as long as B is a subset of the union of all the A events.
  • #1
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 ?
 

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  • #2
tzx9633 said:
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?
 
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  • #3
tzx9633 said:

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?
 

1. What is a Venn diagram and how does it work?

A Venn diagram is a tool used to visually represent relationships between sets of data or concepts. It consists of overlapping circles or other shapes, with each circle representing a different set and the overlapping areas representing the relationships between those sets. It works by organizing data or concepts into categories and showing how they overlap or intersect with one another.

2. How do I create a Venn diagram?

To create a Venn diagram, first identify the sets of data or concepts you want to compare. Then, draw overlapping circles or shapes to represent each set. Label each circle with the name of the set it represents. Finally, fill in the overlapping areas to show the relationships between the sets.

3. Can a Venn diagram have more than three sets?

Yes, a Venn diagram can have any number of sets. However, as the number of sets increases, it may become more difficult to accurately represent all of the relationships between them. In these cases, it may be more helpful to use alternative visual tools, such as Euler diagrams.

4. How is a Venn diagram different from an Euler diagram?

A Venn diagram uses overlapping circles or shapes to represent relationships between sets, while an Euler diagram uses non-overlapping shapes to show relationships. In a Venn diagram, the size and position of the circles can be adjusted to accurately represent the relationships, while in an Euler diagram, the shapes are fixed and do not change in size or position.

5. Can I use a Venn diagram to compare quantitative data?

Yes, a Venn diagram can be used to compare quantitative data. In this case, the circles or shapes would represent ranges of values rather than sets of data. For example, one circle could represent all values between 1-10, while another circle could represent values between 5-15. The overlapping area would then show the values that fall within both ranges.

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