12. Incorrect. The answer is false, not true. To answer this question, firstly you have to define the following events:

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:

P(5,3,1,1) =