An accountant found in a study that receivables fell into four categories:

A: paid on time

B: paid early

C: paid late

D: didn't pay

Of a sample of 120 receivables she found that 35 were paid on time, 40 were paid early, 28 were paid late and the remainder were uncollectable.

a) Using the results from the sample determine the probability of each category.

b) If the accountant had to collect receivables twice a year, construct a tree diagram to show the number of different levels of punctuality clients could display.

c) Use this tree diagram and the probability determined in part (a) to calculate the probability that she should receive at least one payment exactly on time.