In a certain game, an urn contains 6 red, 6 white numbered balls. A ball is drawn at random from the urn.

If this first ball is red, a second ball is drawn from the urn the colour of both balls is recorded.

If, instead, the first ball was white, it is returned to the urn and a second ball is drawn.

Only the colour of this second ball is then recorded.

Either way, after the second ball is drawn and colour recorded, the game stops.

a)Draw a tree diagram describing this experiment.

b)What is the probability that a white ball is drawn sometime during the game?

In the game described in the question above, we now give the player a point each time a red ball is recorded.

What is the expected number of points for this game?