AQA Paper 3 2019 June — Question 14

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2019
SessionJune
TopicConditional Probability
TypeBasic two-way table probability

14 A survey was conducted into the health of 120 teachers. The survey recorded whether or not they had suffered from a range of four health issues in the past year. In addition, their physical exercise level was categorised as low, medium or high.
50 teachers had a low exercise level, 40 teachers had a medium exercise level and 30 teachers had a high exercise level. The results of the survey are shown in the table below.
Low exerciseMedium exerciseHigh exercise
Back trouble14710
Stress38145
Depression921
Headache/Migraine455
14
  1. Find the probability that a randomly selected teacher:
    14
    1. suffers from back trouble and has a high exercise level;
      14
  2. (ii) suffers from depression.
    14
  3. (iii) suffers from stress, given that they have a low exercise level.
    14
  4. For teachers in the survey with a low exercise level, explain why the events 'suffers from back trouble' and 'suffers from stress' are not mutually exclusive.