Given that 𝐴 and 𝐵 are two events in the sample space of a random experiment, where 𝐴 is a subset of 𝐵, determine 𝐴 intersection 𝐵.
One way of representing this sample space is using a Venn diagram. We are told that 𝐴 is a subset of 𝐵. This means that every element of 𝐴 is also an element of 𝐵. In our Venn diagram, the circle representing the elements in 𝐴 is entirely contained within the circle representing the elements of 𝐵. We are asked to determine 𝐴 intersection 𝐵. This is one of our general rules of subsets, which states that if 𝐴 is a subset of 𝐵, then 𝐴 intersection 𝐵 is equal to 𝐴. The correct answer is therefore 𝐴.
Whilst it is not required in this question, it is also worth noting that if 𝐴 is a subset of 𝐵, then 𝐴 union 𝐵 is equal to 𝐵. All the elements in event 𝐴 or event 𝐵 or both are in event 𝐵.