Please show your work!

'Question 4: 'Wheu FE and his girlfriend XF have a child, this child is a boy with probability 1f 2 and a girl 1with probability 13'2, independently of the sex of their other children. F): and HF stop having children as soon as they have three girls or two boys. Consider the random variables [\"3" = the number of ehildren that FE and IF have, G = the number of girls that F151: and HF have. R = the number of boys that F11 and HF have. 1. Determine the eerpeeted values E{C'} and 13(0) 2. We are told that the last ehild FE and KF had was a boy Determine the expected 1values E{B} and E115? and E(C]