4 Rahul has two bags, \(X\) and \(Y\). Bag \(X\) contains 4 red marbles and 2 blue marbles. Bag \(Y\) contains 3 red marbles and 4 blue marbles. Rahul also has a coin which is biased so that the probability of obtaining a head when it is thrown is \(\frac { 1 } { 4 }\). Rahul throws the coin.

• If he obtains a head, he chooses at random a marble from bag \(X\). He notes the colour and replaces the marble in bag \(X\). He then chooses at random a second marble from bag \(X\).
• If he obtains a tail, he chooses at random a marble from bag \(Y\). He notes the colour and discards the marble. He then chooses at random a second marble from bag \(Y\).
  1. Find the probability that the two marbles that Rahul chooses are the same colour.
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  2. Find the probability that the two marbles that Rahul chooses are both from bag \(Y\) given that both marbles are blue.