QUESTION 1

(a) There are three political parties, A, B and C. In a certain year the general public is divided in their support of the three political parties in the ratio 35 : 35 : 30 (A : B: C). The sex distribution of support for the parties is 60 : 40 for A, 50 : 50 for B and 45 : 55 for C, each ratio being male: female. When questioned on a current issue, male - A were 80 : 20 in favour whilst female - A were 70 : 30 in favour. Male - B were 70 : 30 in favour and female - B were 60 : 40 in favour. Male - C were 20 : 80 in favour and female - C were 30 : 70 in favour.

i) Construct a probability tree diagram.

(ii) Find the proportion of the sample who were male - A in favour of the proposal.

iii) If an individual is in favour of the proposition, what is the probability that they are an A supporter?