Stuck on strange conditional probability question

Hi

I have studied conditional probability and can do most of the questions. But this one has me stumped.

A school is divided into 2 parts: Upper school, 400 boys and 200 girls, Lower school, 400 girls and 300 boys. A first pupil is chosen at random from the school. If this pupil comes from the Lower school, a second pupil is chosen from the Upper school; if the first pupil comes from the Upper school, the second pupil is chosen from the Lower school. Find the probability that:

(a) the second pupil chosen will be a girl,

(b) if the second pupil chosen is a boy, he is a member of the Upper school.

I started by drawing up a tree diagram. My calculation for the second pupil being a girl was eg if BG, GG, BG, GG with probs

BG: 8/21

GG: 4/21

BG: 1/7

GG: 4/21

Adding up is: 19/21 (Yes does look too high).

The answer for (a) is 121/273. But how?

The answer for (b) is 49/76 - but I didn't even get onto that one.

Any ideas?

Angus