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

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃(𝐴 βˆͺ 𝐡) = 0.93 and 𝑃(𝐴 βˆ’ 𝐡) = 0.39, find 𝑃(𝐡).

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Video Transcript

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

The first thing we know is the probability of 𝐴 or 𝐡 equals 0.93. But we also know that these are mutually exclusive events, which means the probability of 𝐴 or 𝐡 equals the probability of 𝐴 plus the probability of 𝐡. It also means the probability of 𝐴 and 𝐡 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 𝐡 equals 0.39. This would be the probability of 𝐴 happening and not 𝐡. And that really tells us that the probability of 𝐴 happening is 0.39. We know the probability of 𝐴 plus the probability of 𝐡 equals 0.93. And then we plug in 0.39 for the probability of 𝐴. To solve for 𝐡, we subtract 0.39 from both sides. And we get the probability of 𝐡 is 0.54.

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