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# Frequency trees

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- Use the frequency tree from the Alpha/ Beta/ Gamma exercise above to construct a Venn diagram representing the data.

A group of students sit three tests. Four-fifths of the students pass the first test. 72% of students passed the second test, but only 64% of students passed both the first and second tests. A fifth of the students passed all three tests.

- What percentage of the students passed the first two tests but failed the third?
- Based on the information given, what is the smallest possible number of students in the group?

- 44%
- 25 students

Teacher resources

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Links to past exam questions

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What next?

- P2a – Theoretical probability
- P2b – Relative frequency
- P3a – Expected frequency
- P4a – Properties of probability
- P6a – Enumerating sets and combinations of sets systematically, using tables, grids and Venn diagrams
- P7a – Constructing theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
- P8a – Tree diagrams