Question Video: Describing the Outcomes of the Intersection of Events Represented on a Venn Diagram Mathematics

Video Transcript

In the sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴 and not 𝐵?

The notation 𝐵 bar means not 𝐵. This is also sometimes written as 𝐵 prime. The 𝑛 symbol means the intersection. This means we’re looking for outcomes that occur in event 𝐴 and not in event 𝐵. We can see from our Venn diagram that set 𝐴 contains the numbers three, six, nine, 12, and 15. These are the multiples of three between one and 15. Set 𝐵 contains the numbers four, eight, and 12. These are the multiples of four between one and 15. Only one of these values, the number 12, occurs in both set 𝐴 and set 𝐵.

This is the number in the intersection of the two circles. 12 is a multiple of three and a multiple of four. We can therefore conclude that the outcomes for the event 𝐴 and not 𝐵 are three, six, nine, and 15. These are the numbers that are multiples of three and not multiples of four. The set of outcomes for event 𝐴 and not 𝐵 will be equal to the set of outcomes for event 𝐴 minus the set of outcomes for event 𝐴 and 𝐵. These are the outcomes that only occur in set 𝐴.