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

In the sample space π, for events π΄ and π΅, what is the set of outcomes for the event π΄ not π΅?

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### Video Transcript

In the sample space π, for events π΄ and π΅, what is the set of outcomes for the event π΄ and not π΅?

The notation π΅ bar means not π΅. This is also sometimes written as π΅ prime. The π symbol means the intersection. This means weβre looking for outcomes that occur in event π΄ and not in event π΅. We can see from our Venn diagram that set π΄ contains the numbers three, six, nine, 12, and 15. These are the multiples of three between one and 15. Set π΅ 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 π΄ and set π΅.

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 π΄ and not π΅ 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 π΄ and not π΅ will be equal to the set of outcomes for event π΄ minus the set of outcomes for event π΄ and π΅. These are the outcomes that only occur in set π΄.