Mr. and Mrs. Basu live in a house only with their children. They have three sons and each of the sons has exactly one sister. How many persons live in that house?

Let's list the members living in the house step by step:
1. Parents: Mr. Basu and Mrs. Basu = $2$ persons.
2. Sons: They have $3$ sons = $3$ persons.
3. Daughters/Sisters: The statement says "each of the sons has exactly one sister". This means all the three sons share the same single sister. It does not mean each son has a separate sister. Thus, there is exactly $1$ daughter in the family.

Let's compute the total number of individuals:

$$\text{Total Persons}=2\text{ (Parents)}+3\text{ (Sons)}+1\text{ (Daughter)}=6\text{ persons}$$