Assume identical twins are always of the same sex, equally likely boys or girls. Assume that for fraternal twins the firstborn is equally likely to be a boy or a girl, and so is the secondborn in dependently of the first. Assume that proportion p o of twins are identical. Proportion q = 1 -p fraternal. Find formulae in terms of p for the following probabilities for twins:
a) P(both boys)
b) P(firstborn boy and secondborn girl)
c) P(secondborn girl |firstborn boy)
d) P(secondborn girl |firstborn girl)