An econometrician has hired two undergraduate students (labelled A and B) to enter the data recorded on some forms into a spreadsheet. There are 15 ?elds to be entered into the spreadsheet. The probability of student A entering a value wrong is pA = 0:15, while the probability of student B entering a value wrong is pB = 0:05. Student A is allocated 30% of the forms to enter while student B is allocated the remaining 70% to enter.

a) Find the probability that student A made no mistakes when entering a randomly selected form.

b) Find the probability that student B made no mistakes when entering a randomly selected form.

c) Use your answers from (a) and (b) to calculate the overall proportion of forms that were entered correctly.

d) Calculate the probability that a randomly selected form is entered with exactly 2 mistakes.

e) Suppose that a randomly sampled form was entered with exactly 2 mistakes. Calculate the probability that this form was entered by student A.

f) Suppose instead the econometrician gets both students to enter each form independently. What is the probability that both students will make at least one mistake when entering the same form?