A transformation rotates about the origin by an angle of $45^\circ$ counter-clockwise, then dilates (with center at the origin) by a factor of $\sqrt{2}.$ Find the matrix for this transformation.

There are three bags: a (contains 2 white and 4 red balls), b (8 white, 4 red) and c (1 white 3 red). you select one ball at random from each bag, observe that exactly two are white, but forget which ball came from which bag. what is the probability that you selected a white ball from bag a?