A survey conducted by Roy Morgan Research asked 1116 Australians to nominate health issues they consider important. Sixty per cent of respondents nominated cancer as an important health issue, while only 29% mentioned heart disease. Assume that these percentages are true for the population of Australia and that 25% of all respondents mentioned both cancer and heart disease as important health issues.

(a) What is the probability that a randomly selected Australian nominates either cancer or heart disease or both as important health issues?

(b) What is the probability that a randomly selected Australian nominates either cancer or heart disease but not both as important health issues?

(c) What is the probability that a randomly selected Australian nominates neither cancer nor heart disease as an important health issue?

(d) Construct a probability matrix for this problem and indicate the locations of your answers to parts (a), (b) and (c) on the matrix.