OCR H240/02 — Question 11

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
TopicPrinciple of Inclusion/Exclusion
TypeFinding Set Cardinalities from Constraints

11 Each of the 30 students in a class plays at least one of squash, hockey and tennis.
  • 18 students play squash
  • 19 students play hockey
  • 17 students play tennis
  • 8 students play squash and hockey
  • 9 students play hockey and tennis
  • 11 students play squash and tennis
    1. Find the number of students who play all three sports.
A student is picked at random from the class.
  • Given that this student plays squash, find the probability that this student does not play hockey. Two different students are picked at random from the class, one after the other, without replacement.
  • Given that the first student plays squash, find the probability that the second student plays hockey.