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A Silicon sample $\mathrm{A}$ is doped with $10^{18}$ atoms $/ \mathrm{cm}^{3}$ of Boron. Another sample $\mathrm{B}$ of identical dimensions is doped with $10^{18}$ atoms $/ \mathrm{cm}^{3}$ of Phosphorus. The ratio of electron to hole mobility is $3.$ The ratio of conductivity of the sample $\mathrm{A}$ to $\mathrm{B}$ is

1. $3$
2. $\frac{1}{3}$
3. $\frac{2}{3}$
4. $\frac{3}{2}$