Question Video: Using Venn Diagrams to Determine the Intersection of Two Events Mathematics

The diagram represents the sample space 𝑆 and the events 𝐴, 𝐵, and 𝐶. Determine 𝑃(𝐴 ⋂ 𝐵).

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Video Transcript

The diagram represents the sample space 𝑆 and the events 𝐴, 𝐵, and 𝐶. Determine the probability of 𝐴 intersection 𝐵.

We recall that the intersection of two events 𝐴 and 𝐵 are those outcomes that occur in event 𝐴 and in event 𝐵. On a Venn diagram, this is represented by the overlap of circle 𝐴 and circle 𝐵. We can see from the Venn diagram that the sample space 𝑆 contains the numbers four six, eight, 16, 18, and 19. This is a total of six outcomes. Of these six outcomes, only one appears in the intersection of event 𝐴 and event 𝐵, the number six. We know that the probability of an event occurring can be written as the number of successful outcomes over the number of possible outcomes. This means that the probability of 𝐴 intersection 𝐵 is one out of six. There is a one in six chance of selecting an outcome that is in event 𝐴 and in event 𝐵.

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