Question Video: Determining the Probability of Difference between Two Events Mathematics

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.