### 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 weβre 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΄.