Freddie owns two bags of marbles. Bag $X$ has 7 red marbles and 3 blue marbles, while bag $Y$ has 4 red marbles and 1 blue marble. Freddie picks one bag at random. A marble is then taken at random from that bag and is not put back. One new red marble is added to each bag. After that, a second marble is taken at random from the same bag as the first marble.
(a)[3]
Draw a tree diagram to show this information, and label the probability on every branch.
(b)[4]
Find the probability that the two marbles removed from the bag are the same colour.
(c)[2]
Find the probability that bag $Y$ is selected given that the marbles removed are not the same colour.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct first stage of tree with two branches for bags $X$ and $Y$ with probabilities $\frac{1}{2}$, $\frac{1}{2}$.” …