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.
Let’s begin by recalling what we mean by the set notation in this question. If 𝐴 is a subset of 𝐵, then every element of 𝐴 is also in 𝐵, but 𝐵 has more elements. The set of elements 𝐴 intersection 𝐵 means every element that is in both set 𝐴 and set 𝐵. We can represent the information given in this question in a Venn diagram. The circle representing the elements in set 𝐴 must be entirely contained within the circle representing the elements of set 𝐵. This means that the elements that are in set 𝐴 and set 𝐵 will be all the elements in set 𝐴. The correct answer is 𝐴. If 𝐴 is a subset of 𝐵, then 𝐴 intersection 𝐵 is equal to 𝐴. Likewise, had 𝐵 been a subset of 𝐴, then 𝐴 intersection 𝐵 would be equal to 𝐵.