A survey company asked purchasing managers what traits in a sales representative impressed them most. Seventy-eight per cent selected ‘thoroughness’. Forty per cent responded ‘knowledge of your own product’. The purchasing managers were allowed to list more than one trait. Suppose 27% of the purchasing managers listed both ‘thoroughness’ and ‘knowledge of your own product’ as the traits that impressed them most. A purchasing manager is sampled randomly.

(a) What is the probability that the manager selected ‘thoroughness’ or ‘knowledge of your own product’?

(b) What is the probability that the manager did not select ‘thoroughness’ and did not select ‘knowledge of your own product’?

(c) If it is known that the manager selected ‘thoroughness’, what is the probability that the manager also selected ‘knowledge of your own product’?

(d) What is the probability that the manager did not select ‘thoroughness’ but did select ‘knowledge of your own product’?