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Suppose π΄ and π΅ are two mutually exclusive events.
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Given that the probability of π΄ minus π΅ is 0.52, find the probability of π΄.
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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 donβt belong in set π΅.
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Itβs equivalent to the intersection of π΄ and π΅ complement.
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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΅.
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So we have 0.52 is equal to the probability of π΄ minus the probability of π΄ intersect π΅.
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But weβre given another key piece of information in the question which we havenβt used yet.
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These two events π΄ and π΅ are mutually exclusive.
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We know that for mutually exclusive events, the probability of their intersection is zero because they cannot occur at the same time.
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So, the probability of π΄ is the same as the probability of π΄ minus π΅.
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Itβs 0.52.