The probability for a contractor to get a road contract is 2/3 and to get a building contract is 5/9. The probability to get atleast one contract is 4/5. The probability to get both the contracts is

  R=Road contract

  B= Building contract

$P\left(R\right)=\frac{2}{3},P\left(B\right)=\frac{5}{9},P(R\cup B)=\frac{4}{5}$

$P(R\cap B)=P\left(R\right)+P\left(B\right)-P(R\cup B)$

                   $=\frac{2}{3}+\frac{5}{9}-\frac{4}{5}$

                   $=\frac{30+25-36}{45}$

                   $=\frac{19}{45}$

The probability to get both the contracts is $\frac{19}{45}$