Probability: Intersection and Union of Sets

Hi again, in my last post I introduced 'the idea of' and 'how to calculate' a probability. I welcome any feedback on this thread at anytime via PM.

A set is a collection of objects often identified by a certain characteristic. The notation used for listing a set are these curly brackets. . Sets are often named for the convenience of not having to re-write or repeat a big sentence or group of numbers.

Here's some examples.

The set of numbers on a six sided die (let's call it set A) is

The set of prime numbers between 1 and 10 (let's call it set B) is

Intersection of sets.The intersection of sets is a very important idea in probability. It describes objects that are 'shared' between 2 or more sets.

The notation for intersection is so the intersection between set and is written as

Now let's find a solution for from the two sets defined above.

Recall and , the intersection is simply elements of each set that can be found in both. By inspection we can conclude as these elements are in both AandB.

Union of sets.Equally as important idea of probability is the union of sets. The union describes objects that are in all sets.

The notation for union is so the union of set and is written as

From our example above to find the union of A and B we need list everything (without repetition) that appears in both sets.

By inspection we can conclude as these elements are in both AorB.

Here's some more examples on intersection and union. I have hidden the answers in case you wanted to have a go yourself.

1. Consider the sets and

a) find the intersection of these sets

b) find the union of these sets

Spoiler:

2. Consider the set of letters that make up the name "Victoria" and the set of letters that make up the name "Catherine".

a) find the intersection of these sets

b) find the union of these sets

Spoiler:

3. Consider the sets , and

a) find the intersection of sets M and N

b) find the intersection of sets M and P

c) find the intersection of sets M and N and P

d) find the union of sets M and N

e) find the union of sets M and P

f) find the union of sets M and N and P

Spoiler:

Next post will talk about complementary probability.