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

Suppose 𝐴 and 𝐵 are two mutually exclusive events. Given that 𝑃(𝐴 − 𝐵) = 0.52, find 𝑃(𝐴).

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### Video Transcript

Suppose 𝐴 and 𝐵 are two mutually exclusive events. Given that the probability of 𝐴 minus 𝐵 is 0.52, find the probability of 𝐴.

We recall, first of all, that the event 𝐴 minus 𝐵 contains all the elements in the sample space that belong in set 𝐴 but don’t belong in set 𝐵. It’s equivalent to the intersection of 𝐴 and 𝐵 complement. We also recall a general rule: the probability of 𝐴 minus 𝐵 is equal to the probability of 𝐴 minus the probability of the intersection of 𝐴 and 𝐵. So we have 0.52 is equal to the probability of 𝐴 minus the probability of 𝐴 intersect 𝐵.

But we’re given another key piece of information in the question which we haven’t used yet. These two events 𝐴 and 𝐵 are mutually exclusive. We know that for mutually exclusive events, the probability of their intersection is zero because they cannot occur at the same time. So, the probability of 𝐴 is the same as the probability of 𝐴 minus 𝐵. It’s 0.52.

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