E1: a tax return which was properly filled.
E2: a tax return with errors which favor the taxpayer.
E3: a tax return with errors which favor the government.
E4: a tax return with both kinds of errors.
The probabilities of occurrence of each event are:
p1 = P[E1] = 0.60, p2 = P[E2] = 0.20, p3 = P[E3] = 0.10, p4 = P[E4] = 0.10,
The experiment consists of choosing at random a tax return. The possible outcomes are the mutually exclusive events E1, E2, E3, and E4. The experiment (random process) is repeated ten times. The probabilities are supposed to be constant in the ten trials. Applying the multinomial distribution con n = 10, we have that: