. On a given day a petrol station serves three times as many men as women.

Two types of petrol are available, grade A and grade B.

Customers pay by cash or cheque.

70% of men and 40% of women buy grade A petrol.

Of the men buying grade A petrol, 80% pay by cheque, of the men buying grade B petrol, 60% pay by cheque.

Of the women buying grade A petrol, half pay by cheque, of the women buying grade B petrol, 40% pay by cheque.

Find the probability that (a) a customer buys grade A petrol, (b) a customer pays by cheque, (c) a woman customer pays by cheque, (d) a customer who pays by cheque for grade A petrol is a man