On a given day a petrol station serves three as many men as women. Two types of petrol are available, grade A and grade B. Customers pay by check or...

On a given day a petrol station serves three as many men as women. Two types of petrol are available, grade A and grade B. Customers pay by check or by cash. 70% of the men and 40% of the women buy grade A petrol. of the men buying grade A petrol, 805 pay by check, and of the men buying grade B petrol, 60% pay by check. Of the women buying grade A petrol, half pay by check and of the women buying grade B petrol, 40% pay by check. Find the probability that (i) a customer buys grade A petrol.(ii) a customer buys by check (iii) a woman customer buys by check(iv) a customer who pays by check for grade A petrol is a man.