Question Video: Using the Venn Diagram to Determine the Probability of the Union of Two Events Mathematics • Second Year of Secondary School

Video Transcript

Use the diagram of the sample space 𝑆 to determine the probability of 𝐵 union 𝐶.

The first thing to note is that the U notation used in this question means here 𝐵 or 𝐶, that is, 𝐵 union 𝐶. So we’re looking for the probability that a value chosen at random is in event 𝐵 or event 𝐶. And we note also that events 𝐵 and 𝐶 are mutually exclusive. This means that there is no value or outcome that is common to both. Next, we note that the sample space 𝑆 contains 10 outcomes, so that 𝑆 is the set containing the values 17, five, three, four, 16, 12, 11, seven, 19, and six. And this means that in computing the probability of event 𝐵 or 𝐶, that is, 𝐵 union 𝐶, we’ll divide by 10 that is the total number of elements in our sample space.

If we now highlight in the Venn diagram the event 𝐵 and the event 𝐶, we see that there are a total of six distinct possible outcomes in the region representing event 𝐵 union 𝐶. And these are four, 16, 12, 11, seven, and 19. And since the probability of 𝐵 union 𝐶 is the number of possible outcomes divided by the total number of outcomes, the probability of 𝐵 union 𝐶 is six over 10. And dividing both numerator and denominator by two, this gives us three over five. Given the diagram of the sample space 𝑆 then, the probability of 𝐵 union 𝐶 is three over five, that is, three-fifths.