Octopus Travel studied the types of work-related activity that Australians do while on holiday. Among other things, 20% take their work with them on holiday. Fifteen per cent negotiate new deals or contracts on holiday. Respondents were allowed to select more than one activity. Suppose that, of those who take their work on holiday, 68% negotiate new deals or contracts. One of these survey respondents is selected randomly.

(a) What is the probability that, while on holiday, this respondent negotiated a new deal or contract and took their work?

(b) What is the probability that, while on holiday, this respondent did not take their work and did not negotiate a new deal or contract?

(c) What is the probability that, while on holiday, this respondent took their work given that the respondent negotiated a new deal or contract?

(d) What is the probability that, while on holiday, this respondent did not negotiate a new deal or contract given that the respondent took their work?

(e) What is the probability that, while on holiday, this respondent did not negotiate a new deal or contract given that the respondent did not take their work?

(f) Construct a probability matrix for this problem.