# Video: Determining the Probability of an Event Involving Mutually Exclusive Events

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

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### Video Transcript

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

Here’s what we know about mutually exclusive events. We know that the probability of 𝐴 and 𝐵 happening at the same time is zero. This is because it’s impossible. Mutually exclusive events do not occur at the same time. That would be like saying is today Tuesday or Wednesday. It’s either Tuesday or Wednesday. But it will never be both.

However, we can say that the probability of 𝐴 or 𝐵 occurring is equal to the probability of 𝐴 plus the probability of 𝐵. When we have the statement “the probability that one of the two events occurs,” this is the probability of 𝐴 or 𝐵. Either 𝐴 or 𝐵 happens. So we can plug in 0.18 for the probability of 𝐴 or 𝐵.

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

The probability of 𝐴 is equal to 0.18 divided by six, which equals 0.03. And that means that the probability of event 𝐵 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.