# Question Video: Using the Addition Rule to Determine the Probability of an Event Involving Mutually Exclusive Events

Suppose 𝐴 and 𝐵 are two mutually exclusive events. Given that 𝑃(𝐴 ∪ 𝐵) = 0.93 and 𝑃(𝐴 − 𝐵) = 0.39, find 𝑃(𝐵).

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### Video Transcript

Suppose 𝐴 and 𝐵 are two mutually exclusive events. Given that the probability of 𝐴 or 𝐵 equals 0.93 and the probability of 𝐴 not 𝐵 is equal to 0.39, find the probability of 𝐵.

The first thing we know is the probability of 𝐴 or 𝐵 equals 0.93. But we also know that these are mutually exclusive events, which means the probability of 𝐴 or 𝐵 equals the probability of 𝐴 plus the probability of 𝐵. It also means the probability of 𝐴 and 𝐵 both happening at the same time is zero. We can represent these two mutually exclusive events with two circles that do not overlap.

We’re also given that the probability of 𝐴 minus 𝐵 equals 0.39. This would be the probability of 𝐴 happening and not 𝐵. And that really tells us that the probability of 𝐴 happening is 0.39. We know the probability of 𝐴 plus the probability of 𝐵 equals 0.93. And then we plug in 0.39 for the probability of 𝐴. To solve for 𝐵, we subtract 0.39 from both sides. And we get the probability of 𝐵 is 0.54.