Venn Diagrams

[ged0609]

How would I represent the following situation in a Venn diagram?

At a first interview for a job, candidates are divided into three groups, A, B or C. The probability of being put in group A is 0.5, group B is 0.3 and group C is 0.2. If a candidate is in group A, s/he has a probability of 0.1 of getting a second interview. Candidates in group B have a probability of 0.5 of getting a second interview and candidates in group C have a probability of 0.9 of getting a second interview.

 

[Deleted member 4993]

How would I represent the following situation in a Venn diagram?

At a first interview for a job, candidates are divided into three groups, A, B or C. The probability of being put in group A is 0.5, group B is 0.3 and group C is 0.2. If a candidate is in group A, s/he has a probability of 0.1 of getting a second interview. Candidates in group B have a probability of 0.5 of getting a second interview and candidates in group C have a probability of 0.9 of getting a second interview.

If I were to solve this assignment:

I would divide a circle into three areas without overlap - since the groups A, B & C are mutually exclusive.

At this site we HELP you to find answers - based on your work that you can show us.

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[BigBeachBanana]

It's an odd question to be asked to draw a Venn diagram. You can't represent all with just one Venn Diagram because you have two things going on here: 1) Be in group A, B, or C. 2) Get a second interview.
Is the original question asking you to represent them in a Venn Diagram, or it's something that you want to do?

 

[ged0609]

If I were to solve this assignment:

I would divide a circle into three areas without overlap - since the groups A, B & C are mutually exclusive.

At this site we HELP you to find answers - based on your work that you can show us.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

This is the best I've come up with so far:



However, what doesn't work for me is the space in the middle circle that's not overlapping A, B or C. That should represent people who got a 2nd interview but weren't in any of the groups - and that's an empty set.

 

[Deleted member 4993]

This is the best I've come up with so far:

View attachment 31246

However, what doesn't work for me is the space in the middle circle that's not overlapping A, B or C. That should represent people who got a 2nd interview but weren't in any of the groups - and that's an empty set.

Did the problem statement specify that you have to use a Venn diagram?

Please post the EXACT problem.

 

[BigBeachBanana]

This is the best I've come up with so far:

View attachment 31246

However, what doesn't work for me is the space in the middle circle that's not overlapping A, B or C. That should represent people who got a 2nd interview but weren't in any of the groups - and that's an empty set.

As I stated before, it's not possible to draw a Venn diagram. If you're having trouble answering the question without the use of a Venn diagram, we can help you with that. Please do as @Subhotosh Khan requested, post the original question, and state why do you need a Venn diagram?

 

[Dr.Peterson]

This is the best I've come up with so far:

View attachment 31246

However, what doesn't work for me is the space in the middle circle that's not overlapping A, B or C. That should represent people who got a 2nd interview but weren't in any of the groups - and that's an empty set.

It's possible to use your diagram in solving the problem, though it is not an ideal representation.

The regions you have not labeled contain 0 people; that's perfectly legal in a Venn diagram. Write 0 in the middle, and 0 on the outside, to show that everyone is in A, B, or C.

But the numbers you wrote are the conditional probabilities of being in the inner circle given that you are in a given one of A, B, or C. If you include (perhaps next to each letter) the probability of being in each of the latter, and then use the definition of conditional probability to modify all the numbers you wrote, you can make sense of this.