Question Video: Finding the Union of Two Events Given That One of Them Is a Subset of the Other Mathematics

Suppose 𝐴 and 𝐵 are events such that 𝐵 ⊂ 𝐴. Determine 𝐴 ∪ 𝐵.

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Video Transcript

Suppose 𝐴 and 𝐵 are events such that 𝐵 is a subset of 𝐴. Determine 𝐴 union 𝐵.

We will begin by recalling what the set notation in this question means. If 𝐵 is a subset of 𝐴, we know that every element of 𝐵 is in 𝐴 and 𝐴 has more elements. The union of events 𝐴 and 𝐵 contains every element in 𝐴 or 𝐵 or in both 𝐴 and 𝐵. We can represent this information on a Venn diagram as shown, where the circle representing event 𝐵 is entirely contained within the circle representing event 𝐴. As already stated, the union of events 𝐴 and 𝐵 will be anything inside circle 𝐴 or in circle 𝐵 or in both. In this question, since 𝐵 is a subset of 𝐴, then 𝐴 union 𝐵 is simply equal to 𝐴.

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