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

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃(𝐴 βˆ’ 𝐡) = 0.52, find 𝑃(𝐴).

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Video Transcript

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

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

But we’re given another key piece of information in the question which we haven’t used yet. These two events 𝐴 and 𝐡 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 𝐡. It’s 0.52.

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