5. A netball team are in a league with three other teams from which one team will progress to the next stage of the competition. The team's coach estimates their chances of winning each of their three matches in the league to be \(0.6,0.5\) and 0.3 respectively, and believes these probabilities to be independent of each other.

1. Show that the probability of the team winning exactly two of their three matches is 0.36
   (4 marks)
   Let the random variable \(W\) be the number of matches that the team win in the league.
2. Find the probability distribution of \(W\).
3. Find \(\mathrm { E } ( W )\) and \(\operatorname { Var } ( W )\).
4. Comment on the coach's assumption that the probabilities of success in each of the three matches are independent.
   (2 marks)