6 A small farm has 5 ducks and 2 geese. Four of these birds are to be chosen at random. The random variable \(X\) represents the number of geese chosen.
- Draw up the probability distribution of \(X\).
- Show that \(\mathrm { E } ( X ) = \frac { 8 } { 7 }\) and calculate \(\operatorname { Var } ( X )\).
- When the farmer's dog is let loose, it chases either the ducks with probability \(\frac { 3 } { 5 }\) or the geese with probability \(\frac { 2 } { 5 }\). If the dog chases the ducks there is a probability of \(\frac { 1 } { 10 }\) that they will attack the dog. If the dog chases the geese there is a probability of \(\frac { 3 } { 4 }\) that they will attack the dog. Given that the dog is not attacked, find the probability that it was chasing the geese.