Tree diagram for a box chosen by spinner and a counter drawn from it, with total and reverse conditional probabilities and expected winnings

In a game at a school fair, a fair four-sided spinner numbered \(1\), \(2\), \(3\) and \(4\) is spun once. If the spinner shows \(4\), box \(S\) is used; otherwise box \(T\) is used. Box \(S\) holds \(3\) blue counters \((B)\) and \(1\) yellow counter \((Y)\). Box \(T\) holds \(2\) blue counters and \(6\) yellow counters. One counter is then taken at random from the box that is used.

1. Copy and complete the tree diagram below.[3]

2. Find
   1. the probability that box \(S\) is used and a yellow counter is taken;
   2. the probability that a yellow counter is taken;
   3. the probability that box \(S\) was used, given that a yellow counter is taken.[7]
3. A player receives \(4\) dollars for a blue counter and \(1\) dollar for a yellow counter. Find the player's expected winnings from one game.[4]