### Video Transcript

Suppose π΄ and π΅ are two
events. Given that π΄ intersection π΅ is
the empty set, the probability of π΄ prime is 0.66, and the probability of π΅ prime
is 0.79, find the probability of π΅ minus π΄.

Before trying to answer this
question, letβs recall some of the notation. We know that π΄ prime and π΅ prime
are the complement of events π΄ and π΅, respectively. And we also know that the
probability of the complement of event π΄ is equal to one minus the probability of
event π΄. Using the information given, we can
therefore calculate the probability of event π΄ along with the probability of event
π΅.

Firstly, we have 0.66 is equal to
one minus the probability of π΄. Rearranging this equation, we have
the probability of π΄ is equal to one minus 0.66. This is equal to 0.34. In the same way, 0.79 is equal to
one minus the probability of event π΅. The probability of π΅ is therefore
equal to one minus 0.79, which is equal to 0.21.

We are also told that π΄
intersection π΅ is equal to the empty set. This means that there are no
elements in event π΄ and event π΅. And we can therefore say that the
two events are mutually exclusive. And the probability of π΄
intersection π΅ is therefore equal to zero. When representing this on a Venn
diagram, there is no overlap as shown. We can fill in the fact that the
probability of event π΄ is 0.34 and the probability of event π΅ is 0.21. We can complete the Venn diagram by
filling in the probability that neither event π΄ nor event π΅ occur. This is equal to 0.45.

We are asked to find the
probability of π΅ minus π΄. And using the difference formula,
we know this is equal to the probability of π΅ minus the probability of π΄
intersection π΅. Substituting in the values we know,
this is equal to 0.21 minus zero, which is just equal to 0.21. This leads us onto an important
rule. If two events π΄ and π΅ are
mutually exclusive, then the probability of π΅ minus π΄ is simply equal to the
probability of π΅. Likewise, the probability of π΄
minus π΅ is equal to the probability of π΄.