# Question Video: Describing the Outcomes of the Complement of an Event 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΄ bar?

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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΄ bar?

The event π΄ bar means those values that are not in π΄. In this question, we have five values β three, six, nine, 12, and 15 β that are in event π΄. This means that all the other values β four and eight that are in event π΅, along with one, two, five, seven, 10, 11, 13, and 14 that are neither in event π΄ or event π΅ β are not in π΄. The correct set of outcomes is therefore the 10 values one, two, four, five, seven, eight, 10, 11, 13, and 14.

Whilst weβre not asked to in this question, we could use the numbers to work out what the events π΄ and π΅ are. The sample space S contains the integers from one to 15. Event π΄, the numbers three, six, nine, 12, and 15 are the multiples of three. Event π΅, on the other hand, four, eight, and 12 are the multiples of four between one and 15. The number 12 occurs in both events as it is a multiple of three and a multiple of four. The eight numbers outside of the circles are neither multiples of three or multiples of four. This means that the set of outcomes π΄ bar are the set of numbers that are not multiples of three between one and 15.