The propagation step of a free radical copolymerization is represented by the following possible reaction steps:
$\text{P1}$: $M_{1}^{*}+M_{1} \rightarrow M_{1}^{*}, \quad$ rate constant $=k_{11}$
$\text{P2}$: $M_{1}^{*}+M_{2} \rightarrow M_{2}^{*}, \quad$ rate constant $=k_{12}$
$\text{P3}$: $M_{2}^{*}+M_{1} \rightarrow M_{1}^{*}, \quad$ rate constant $=k_{21}$
$\text{P4}$: $M_{2}^{*}+M_{2} \rightarrow M_{2}^{*}, \quad$ rate constant $=k_{22}$
where, $M_{1}$ and $M_{2}$ are two monomers and $M_{1}^{*}$ and $M_{2}^{*}$ are the active radicals of $M_{1}$ and $M_{2}$, respectively. $k_{i j}(i, j=1,2)$ represents the rate constant of each step as shown above.
If the reactivity ratios of $M_{1}$ and $M_{2}$ are expressed as: $r_{1}=k_{11} / k_{12}$ and $r_{2}=k_{22} / k_{21}$, respectively, and feed mole ratio, $F$ is expressed as $F=\left[M_{1}\right] /\left[M_{2}\right]$ $\text{(where, $\left[M_{1}\right]$ and $\left[M_{2}\right]$ are the concentrations of $M_{1}$ and $M_{2}$, respectively)}$, the probability of the reaction $P2$ is ___________.
- $\frac{r_{1}}{r_{1} F+1}$
- $\frac{1}{r_{1} F+1}$
- $\frac{1}{r_{2}+F}$
- $\frac{r_{2}}{F+r_{2}}$
