Video Transcript
Suppose that 𝐴 and 𝐵 are mutually
exclusive events. Determine the probability of 𝐴
intersects 𝐵.
In this question, we are given two
mutually exclusive events 𝐴 and 𝐵 and asked to determine the probability of 𝐴
intersects 𝐵, that is, the probability that both events occur. To answer this question, we can
start by recalling that we say that two events 𝐴 and 𝐵 are mutually exclusive if
they cannot both occur. In other words, the intersection of
both events is the empty set.
This is enough information to
answer the question. If both events 𝐴 and 𝐵 cannot
happen at the same time since they are mutually exclusive, then the probability of
both events occurring must be zero since it is impossible for both of them to
occur. More formally, we can think of this
in terms of the number of outcomes where both 𝐴 and 𝐵 occur divided by the total
number of possible outcomes. Once again, we know there are no
outcomes where both 𝐴 and 𝐵 occur since they are mutually exclusive. So, the probability must be
zero.
