Given the equations $3P(A) = \frac{3}{5}$ and $P(B) = \frac{3}{5}$. From $3P(A) = \frac{3}{5}$, we get $P(A) = \frac{1}{5}$.
Using the conditional probability formula $P(A|B) = \frac{P(A \cap B)}{P(B)}$, we substitute the known values: $$\frac{2}{3} = \frac{P(A \cap B)}{3/5}$$ $$P(A \cap B) = \frac{2}{3} \times \frac{3}{5} = \frac{2}{5}$$
Using the addition theorem of probability: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ $$P(A \cup B) = \frac{1}{5} + \frac{3}{5} - \frac{2}{5}$$ $$P(A \cup B) = \frac{1+3-2}{5} = \frac{2}{5}$$
Final Answer: 2/5
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