H2 Mathematics A Level [Modified] Q2

A bag contains \(4\) red, \(5\) blue, and \(6\) green balls. The balls are indistinguishable except for their colour. A trial consists of drawing a ball at random from the bag, noting its colour and replacing it in the bag. A game is played by performing \(10\) trials in all.

The player receives \(\$0.50\) for every blue ball drawn in a game. He receives nothing if balls of other colours are drawn.

1. Find the probability that, in a game, he receives more than \(\$2.50\).[2]
2. If \(20\) players are randomly chosen, find the expected number of players who will receive more than \(\$2.50\).[2]
3. Find also the amount a player is most likely to receive.[2]
4. Tom and Jerry both played the game. Given that they both received more than \(\$2.50\), find the probability that Tom received at least \(\$1.50\) more than Jerry.[3]