We need to calculate $33\frac{1}{3}\%$ of $0.12$ of $3\frac{1}{3}$.

1. Problem Description

We need to calculate $33\frac{1}{3}\%$ of $0.12$ of $3\frac{1}{3}$.

2. Solution Steps

First, let's convert the mixed numbers to improper fractions and the percentage to a fraction.

$33\frac{1}{3} = \frac{33 \times 3 + 1}{3} = \frac{99+1}{3} = \frac{100}{3}$

$3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9+1}{3} = \frac{10}{3}$

$33\frac{1}{3}\% = \frac{100}{3}\% = \frac{100}{3} \times \frac{1}{100} = \frac{1}{3}$

Now, we need to calculate $\frac{1}{3}$ of $0.12$ of $\frac{10}{3}$. This translates to the following expression:

$\frac{1}{3} \times 0.12 \times \frac{10}{3}$

Convert $0.12$ to a fraction: $0.12 = \frac{12}{100} = \frac{3}{25}$.

Substitute this fraction into the expression:

$\frac{1}{3} \times \frac{3}{25} \times \frac{10}{3}$

Simplify the expression:

$\frac{1}{3} \times \frac{3}{25} \times \frac{10}{3} = \frac{1 \times 3 \times 10}{3 \times 25 \times 3} = \frac{30}{225}$

Reduce the fraction:

$\frac{30}{225} = \frac{6}{45} = \frac{2}{15}$

3. Final Answer

$\frac{2}{15}$