The probability that the first critic favours the book is $\mathrm{P}(\mathrm{A})=\frac{2}{2+5}=\frac{2}{7}$
$$
\therefore \quad \mathrm{P}\left(\mathrm{A}^{\prime}\right)=1-\frac{2}{7}=\frac{5}{7}
$$

The probability that the second critic favours the book is $\mathrm{P}(\mathrm{B})=\frac{3}{3+4}=\frac{3}{7}$
$$
\therefore \quad \mathrm{P}\left(\mathrm{B}^{\prime}\right)=1-\frac{3}{7}=\frac{4}{7}
$$

The probability that the third critic favours the book is $\mathrm{P}(\mathrm{C})=\frac{4}{4+3}=\frac{4}{7}$
$$
\therefore \quad \mathrm{P}\left(\mathrm{C}^{\prime}\right)=1-\frac{4}{7}=\frac{3}{7}
$$
$\therefore \quad$ Majority will be in favour of the book if at least two critics favour the book.
Hence, the probability is
$\begin{aligned} & \mathrm{P}\left(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}^{\prime}\right)+\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}^{\prime} \cap \mathrm{C}\right) \\ & \quad+\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B} \cap \mathrm{C}\right)+\mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}) \\ & =\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) \cdot \mathrm{P}\left(\mathrm{C}^{\prime}\right)+\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}\left(\mathrm{B}^{\prime}\right) \cdot \mathrm{P}(\mathrm{C}) \\ & +\mathrm{P}\left(\mathrm{A}^{\prime}\right) \cdot \mathrm{P}(\mathrm{B}) \cdot \mathrm{P}(\mathrm{C})+\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) \cdot \mathrm{P}(\mathrm{C})\end{aligned}$
$\begin{aligned} & =\frac{2}{7} \times \frac{3}{7} \times \frac{3}{7}+\frac{2}{7} \times \frac{4}{7} \times \frac{4}{7}+\frac{5}{7} \times \frac{3}{7} \times \frac{4}{7}+\frac{2}{7} \times \frac{3}{7} \times \frac{4}{7} \\ & =\frac{18}{343}+\frac{32}{343}+\frac{60}{343}+\frac{24}{343} \\ & =\frac{134}{343}\end{aligned}$