68% of a small business' transactions are cash and 32% are credit. Of the cash transactions, 57% are for goods and 43% of services. Of the credit transactions, 65% are goods and 35% for services.
a) Find the probability that a transaction is a cash transaction.
b) Find the probability that a transaction is for goods given that it us a cash transaction.
c) Find the probability that a transaction is a cash transaction and that it is for goods.
d) Suppose it is known that a transaction is for goods. Use the tabular form of Bayes theorem to find the probability that it is a cash transaction.