Agreement of Inaccurate Arithmeticians

$A$ and $B$ are two inaccurate arithmeticians whose chance of solving a given question correctly are $\frac{1}{8}$ and $\frac{1}{12}$ respectively; if they obtain the same result, and if it is $1000$ to $1$ against their making the same mistake, find the chance that the result is correct.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXXII. Probability, Examples XXXII.d, No. 18