### Video Transcript

Suppose that π΄ and π΅ are two
mutually exclusive events. The probability of event π΅
occurring is five times that of the event π΄ occurring. Given that the probability of one
of these two events occurs is 0.18, find the probability of event π΄ occurring.

Hereβs what we know about mutually
exclusive events. We know that the probability of π΄
and π΅ happening at the same time is zero. This is because itβs
impossible. Mutually exclusive events do not
occur at the same time. That would be like saying is today
Tuesday or Wednesday. Itβs either Tuesday or
Wednesday. But it will never be both.

However, we can say that the
probability of π΄ or π΅ occurring is equal to the probability of π΄ plus the
probability of π΅. When we have the statement βthe
probability that one of the two events occurs,β this is the probability of π΄ or
π΅. Either π΄ or π΅ happens. So we can plug in 0.18 for the
probability of π΄ or π΅.

But we also know that the
probability of event π΅ is five times the probability of event π΄. So what we can do is we can plug in
five times the probability of event π΄ in for the probability of event π΅. Probability of π΄ plus five times
the probability of π΄ equals six times the probability of π΄. To find the probability of π΄, we
would then need to divide both sides of the equation by six.

The probability of π΄ is equal to
0.18 divided by six, which equals 0.03. And that means that the probability
of event π΅ equals five times 0.03, 0.15. And if we wanted to check does 0.03
plus 0.15 add up to 0.18? It does.