(i)[3]
Construct the probability distribution for $X$.
(ii)[3]
Demonstrate that $\text{E}(X) = \tfrac{8}{7}$ and determine $\text{Var}(X)$.
(iii)[4]
When the farmer’s dog is released, it either chases the ducks with probability $\tfrac{3}{5}$ or chases the geese with probability $\tfrac{2}{5}$. If it chases the ducks, there is a probability of $\tfrac{1}{10}$ that they will attack the dog. If it chases the geese, there is a probability of $\tfrac{3}{4}$ that they will attack the dog. Given that the dog is not attacked, determine the probability that it was chasing the geese.