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

Suppose π΄ and π΅ are two mutually exclusive events. Given that π(π΄ β π΅) = 0.52, find π(π΄).

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### Video Transcript

Suppose π΄ and π΅ are two mutually exclusive events. Given that the probability of π΄ minus π΅ is 0.52, find the probability of π΄.

We recall, first of all, that the event π΄ minus π΅ contains all the elements in the sample space that belong in set π΄ but donβt belong in set π΅. Itβs equivalent to the intersection of π΄ and π΅ complement. We also recall a general rule: the probability of π΄ minus π΅ is equal to the probability of π΄ minus the probability of the intersection of π΄ and π΅. So we have 0.52 is equal to the probability of π΄ minus the probability of π΄ intersect π΅.

But weβre given another key piece of information in the question which we havenβt used yet. These two events π΄ and π΅ 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 π΄ is the same as the probability of π΄ minus π΅. Itβs 0.52.