2025 IGCSE 0580 May/June P42 Q22

\(\mathcal E=\{\text{number of students in a class}\hspace{0.15em}\}\)

\(G=\{\text{number of students who study geography}\hspace{0.15em}\}\)

\(H=\{\text{number of students who study history}\hspace{0.15em}\}\)

The Venn diagram shows information about the 33 students in a class.

1. One of the students in the class is picked at random.
   Find the probability that this student
   1. does not study geography and does not study history[1]
   2. studies geography and studies history.[1]
2. Two of the students who study history are picked at random.
   Find the probability that one student also studies geography and one student does not study geography.[3]