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5 V) Venn Diagrams – Part 5: Probability Notation
5 V) Venn Diagrams – Part 5: Probability Notation
In this section we are going to go through the probability notation. It is worth getting all of these rules down on a revision card because they are quite easy to forget:
I am now going to go through these different areas on the Venn diagram below.
- ⋂ means intersection and it can be essentially viewed as “and”. For example, if we were asked to find P(A ⋂ B), we would be finding the probability of choosing an individual that is in A and in B.
- ∪ means union and it can be essentially viewed as “or”. For example, if we were asked to find P(A ∪ B), we would be finding the probability of choosing an individual that is in A or B.
- ’ means not. For example, if we were asked to find P(A’), we would be finding the probability of choosing an individual that does not like A.
I am now going to go through these different areas on the Venn diagram below.
A ⋂ B
This stands for people that are in the A circle and the B circle. Therefore, it is the area of the intersection of the two circles.
This stands for people that are in the A circle and the B circle. Therefore, it is the area of the intersection of the two circles.
A ∪ B
This stands for people that are in A or B. There are 3 areas on the diagram whereby people are in A or B. These three areas are:
These areas are shown on the Venn diagram below.
This stands for people that are in A or B. There are 3 areas on the diagram whereby people are in A or B. These three areas are:
- In A and not B
- In A and B
- In B and not A
These areas are shown on the Venn diagram below.
B’
This stands for individuals that are not in B. These people will be outside the B circle.
This stands for individuals that are not in B. These people will be outside the B circle.
A ⋂ B’
This stands for individuals that are in A and are not in B. There is only one section on the diagram that represents this, and it is shaded on the diagram below.
This stands for individuals that are in A and are not in B. There is only one section on the diagram that represents this, and it is shaded on the diagram below.
A’ ⋂ B
This stands for individuals that are not in A and are in B. There is only one section on the diagram that represents this, and it is shaded on the diagram below.
This stands for individuals that are not in A and are in B. There is only one section on the diagram that represents this, and it is shaded on the diagram below.
A ∪ B'
This stands for individuals that are in A or not B. I am going to work out the parts that are in A, and then the parts that are not in B seperately.
If you are in A, you are in the A circle. There are two parts on the Venn diagram where this is the case. One is where you are in A and not B. The other is where you are in A and B. These areas are shaded in blue on the diagram below.
This stands for individuals that are in A or not B. I am going to work out the parts that are in A, and then the parts that are not in B seperately.
If you are in A, you are in the A circle. There are two parts on the Venn diagram where this is the case. One is where you are in A and not B. The other is where you are in A and B. These areas are shaded in blue on the diagram below.
Now let’s find the parts on the diagram that are not in B. If you are not in B, you are outside of the B circle. There are two parts on the Venn diagram where this is the case. One is where you are in A and not B. The other is where you are not in A and not in B. I have shaded these areas in yellow on the diagram below (the part where the shading overlaps looks green).
We were looking for the parts of the Venn diagram that are in A or not in B. As we are working with or, the parts of the Venn diagram for A ∪ B' is all of the shaded area on the above diagram (both the blue and yellow shaded areas).
Personally, I have always found these types of “or” questions quite tricky as it feels as if you are shading parts of the diagram that are wrong. This feeling can be overcome by working with the first component in what we are looking for (for this example, it was being in A) and then the second component in what we are looking for (for this example, it was not being in B). We then combine the areas because we are working with or. If you answer these questions like this, they should seem considerable easier.
Personally, I have always found these types of “or” questions quite tricky as it feels as if you are shading parts of the diagram that are wrong. This feeling can be overcome by working with the first component in what we are looking for (for this example, it was being in A) and then the second component in what we are looking for (for this example, it was not being in B). We then combine the areas because we are working with or. If you answer these questions like this, they should seem considerable easier.
A' ∪ B
This stands for individuals that are not in A or in B. I am going to work out the parts that are not in A, and then the parts that are in B seperately.
If you are not in A, you are outside of the A circle. There are two parts on the Venn diagram where this is the case. One is where you are in B and not A. The other is where you are not in A and not in B. These areas are shaded in blue on the diagram below.
This stands for individuals that are not in A or in B. I am going to work out the parts that are not in A, and then the parts that are in B seperately.
If you are not in A, you are outside of the A circle. There are two parts on the Venn diagram where this is the case. One is where you are in B and not A. The other is where you are not in A and not in B. These areas are shaded in blue on the diagram below.
If you are in B, you are in the B circle. There are two parts on the Venn diagram where this is the case. One is where you are in B and not in A. The other is where you are in B and in A. I have shaded these areas in yellow on the diagram below (the part where the shading overlaps looks green).
We were looking for the parts of the Venn diagram that are not in A or in B. As we are working with or, the parts of the Venn diagram for A' ∪ B is all of the shaded area on the above diagram (both the blue and yellow shaded areas).
End Note
The best way to answer questions like this is to deal with each of the components that you are asked seperately. For example, if we were given A’ ⋂ B, you would work with what A’ means (not A), then what ⋂ means (and), and then finally what B means (in B). After you have gone through each of the components, you can then find the area or probability that you are looking for.
The best way to answer questions like this is to deal with each of the components that you are asked seperately. For example, if we were given A’ ⋂ B, you would work with what A’ means (not A), then what ⋂ means (and), and then finally what B means (in B). After you have gone through each of the components, you can then find the area or probability that you are looking for.