Video Transcript
Suppose 𝐴 and 𝐵 are two
events. Given that the probability of 𝐴 is
0.3 and the probability of 𝐴 intersection 𝐵 is 0.03, determine the probability of
𝐴 minus 𝐵.
Let’s begin by recalling the
notation shown in this question. Firstly, we have the intersection
of events 𝐴 and 𝐵. This is all the outcomes that occur
in event 𝐴 and in event 𝐵. This can be represented on a Venn
diagram as shown. The probability of 𝐴 minus 𝐵 is
known as the difference and could be represented on a Venn diagram as shown. It is all of the outcomes in event
𝐴 that are not in event 𝐵.
We recall that the difference
formula states that the probability of 𝐴 minus 𝐵 is equal to the probability of 𝐴
minus the probability of 𝐴 intersection 𝐵. Using the values given in the
question, the probability of 𝐴 minus 𝐵 is equal to 0.3 minus 0.03. This is equal to 0.27.
