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.
