2026 EVG P2 Q5

Using set notation, write down a statement to describe the set \(A\cap B\).[1]

Complete the Venn diagram to represent sets A and B. Shade the region which represents \(A^{\prime}\cap B\).[2]

A number, q, is chosen at random from \(A^{\prime}\cap B\). Find the probability that \(q\notin A^{\prime}\cap B\).[1]

There are y students who study both Biology and Physics. Two students are selected at random. The probability that they both study Biology and Physics is \(63/130\). Write an equation to represent this information and show that it simplifies to \(y^2-y-756=0\).[2]

Solve \(y^2-y-756=0\) using factorisation.[2]

One student is selected at random. The probability that this student does not study Physics is \(1/8\). Complete the table about the class of 40 students.[2]