Each customer at a supermarket pays by one of cash, cheque or credit card. The probability of a randomly selected customer paying by cash is 0.54 and by cheque is 0.18.

(a) Determine the probability of a randomly selected customer paying by credit card. Three customers are selected at random.

(b) Find the probability of (i) all three paying by cash, (ii) exactly one paying by cheque, (iii) one paying by cash, one by cheque and one by credit card. The probability that the amount payable exceeds 30 is 0.26. If the amount payable does exceed 30, then the probability of it being paid by cheque is 0.28.

(c) Find the probability that a randomly selected customer pays more than 30 and pays by cheque.

(d) Hence find the probability that a randomly selected customer pays more than 30, given that the customer pays by cheque. (AEB)