Step-by-step Solution:

\[ \text{Let } n_B \text{ and } n_{A \cap B} \text{ denote the number of outcomes favourable to B and A } \cap B \text{ respectively.} \] \[ \text{As A and B are independent,} \] \[ P(A \cap B) = P(A) P(B) \] \[ \Rightarrow \frac{n_{A \cap B}}{10} = \frac{4}{10} \times \frac{n_B}{10} \] \[ \Rightarrow 5n_{A \cap B} = 2n_B \] \[ \Rightarrow 5 \mid n_B \] \[ \Rightarrow n_B = 5 \text{ or } 10. \quad [\because 1 \leq n_B \leq 10] \]