## Exam-Style Question on Sets## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 190. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

A driving test has two sections, practical(p) and theory(t). One day everyone who took the test passed at least one section. 77% passed the practical section and 81% passed the theory section.

(a) Represent this information on a Venn diagram showing the percentage of candidates in each section of the diagram.

One person is chosen at random from all the people who took the test that day. What is the probability that this person:

(b) passed the practical section, given that they passed the theory section,

(c) passed the theory section, given that they passed only one section?

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