# Question Video: Determining the Probability of an Event Involving Mutually Exclusive Events Mathematics • 10th Grade

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 that one of the two events occurs is 0.18, find the probability of event π΄ occurring.

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### 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.

Hereβs 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 itβs impossible. Mutually exclusive events do not occur at the same time. That would be like saying is today Tuesday or Wednesday. Itβs 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 βthe 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.