5 In a recent survey, a large number of working people were asked whether they worked full-time or part-time, with part-time being defined as less than 25 hours per week. One of the respondents is selected at random.
- \(W\) is the event that this person works part-time.
- \(F\) is the event that this person is female.
You are given that \(\mathrm { P } ( W ) = 0.14 , \mathrm { P } ( F ) = 0.41\) and \(\mathrm { P } ( W \cap F ) = 0.11\).
- Draw a Venn diagram showing the events \(W\) and \(F\), and fill in the probability corresponding to each of the four regions of your diagram.
- Determine whether the events \(W\) and \(F\) are independent.
- Find \(\mathrm { P } ( W \mid F )\) and explain what this probability represents.