Question Video: Describing the Outcomes of the Complement of an Event Represented on a Venn Diagram Mathematics • Second Year of Secondary School

Video Transcript

In the sample space 𝑆 for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐵 bar?

Let’s begin by considering the notation in the question. 𝐵 bar, also sometimes written 𝐵 prime, is the complement of event 𝐵. We recall that the complement of an event is the set of elements not in that event. In this question, we are looking for the set of elements that are not in event 𝐵.

Event 𝐵 contains the outcomes four, eight, and 12. These are the numbers in the four times table between one and 15. This means that the complement of event 𝐵 contains all the outcomes not in event 𝐵. These are one, two, three, five, six, seven, nine, 10, 11, 13, 14, and 15. There are 12 outcomes for this event.

Whilst it is not required for this question, it is worth noting that event 𝐴 contains all the elements in the three times table between one and 15 inclusive. These are three, six, nine, 12, and 15. The intersection of events 𝐴 and 𝐵 contains just one element, the number 12, as this is the only number in both the three and four times table between one and 15.