Sam and Tom are taking part in a game that uses a bag with $5$ white discs and $3$ red discs. They alternate turns, each time taking one disc at random from the bag. Once a disc has been taken out, it is not put back into the bag. The game stops immediately when one player has taken two red discs from the bag. That player is the winner. Sam takes the first disc.
(a)[2]
Find the probability that Tom takes a red disc on his first turn.
(b)[4]
Find the probability that Tom wins the game on his second turn.
(c)[2]
Find the probability that Sam takes a red disc on his first turn given that Tom wins the game on his second turn.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct probability expression for $P(\text{SR then TR})+P(\text{SW then TR})$” …