Question Video: Finding the Intersection of Two Events Mathematics

Given that 𝐴 and 𝐡 are two events in the sample space of a random experiment, where 𝐴 βŠ‚ 𝐡, determine 𝐴 ∩ 𝐡.

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Video Transcript

Given that 𝐴 and 𝐡 are two events in the sample space of a random experiment, where 𝐴 is a subset of 𝐡, determine 𝐴 intersection 𝐡.

Let’s begin by recalling what we mean by the set notation in this question. If 𝐴 is a subset of 𝐡, then every element of 𝐴 is also in 𝐡, but 𝐡 has more elements. The set of elements 𝐴 intersection 𝐡 means every element that is in both set 𝐴 and set 𝐡. 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 𝐡. This means that the elements that are in set 𝐴 and set 𝐡 will be all the elements in set 𝐴. The correct answer is 𝐴. If 𝐴 is a subset of 𝐡, then 𝐴 intersection 𝐡 is equal to 𝐴. Likewise, had 𝐡 been a subset of 𝐴, then 𝐴 intersection 𝐡 would be equal to 𝐡.

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