Venn Diagrams - Corbettmaths

section, then we know that it is 81 in this circle and it says to represent this information in the Venn diagram. Now, to start, we know that no one failed in both sections, so let's put zero on the outside. This may seem a little difficult because we don't have much information to figure out what's in the middle, but we actually have enough information. We know that these four numbers are all together in this Venn diagram. If we had this number, this number, and this zero, now we know that they must add up to 100, so it must mean that this number plus this number plus this number would be 100.

We also know that the 70 within the theory section, uh, that means inside this circle it would be 70, so there would be 70 here, that must mean there would be 30 there, we could have looked the other way and we could have looked at 81 for the practical section and worked on that and then we could have solved it, but that's the same thing, okay, it says 81 beyond the practical section, now within this practical section, we know that there are 81 percent, if we have 30 here, that was something that we would have 51 in the middle because I want to say 81 in total. circle and finally because we know it's going to be 100 30 50 the 81 of one leaves us 19 there and we just check that they add up to give us 70, so we have completed the Venn diagram now the next question is very important, it is a fact Since the question says that a student is selected at random, calculate the probability that the person has passed the exam, oh, sorry, calculate the probability that this person has passed the theoretical section, given that he passed the practical section, like this that first of all we know that this person passed the practical section, okay, so we know that we are inside the circle, they passed the practical section, so we are just considering these two numbers here, okay, it says what is the probability that they pass? the theory section so that the theory section passes. will be this 51. so it will be 51 of the 81 that are inside the server that is inside that circle, so the answer would be 51 of 81 and that's it.