A $0.1 \textit{ mL}$ aliquot of a bacteriophage stock having a concentration of $4 \times 10^9 \textit{ phages mL}^{-1}$ is added to $0.5 \textit{ mL}$ of $\textit{E. coli}$ culture having a concentration of $2 \times 10^8 \textit{ cells mL}^{-1}$. The multiplicity of infection is ________