a probability question ...?

Question

a cage holds two litters of rats. one litter has 3 female and 4 male. and other litter has two female and 6 male. a random selection of two rats is made. find as fraction the prob that the two rats are
i) from the same litter.
ii) of the same sex)
iii) the same litter and of the same sex
iv) from the same litter give that they are the same sex

Been trying to work this out for a while and i get the wrong results :((

Answer 1

i)
P(Same litter)
= P(Both from first litter OR both from second litter)
= P(Both from first litter) + P(Both from second litter) since these events are mutually exclusive.
= P(1st is from first litter AND 2nd is from first litter) + P(1st is from second litter AND 2nd is from second litter)
= P(1st is from first litter)P(2nd is from first litter|1st is from first litter) + P(1st is from second litter|2nd is from second litter) using the general multiplication rule.
= (7/15)(6/14) + (8/15)(7/14)
= 7/15

ii)

P(Both same sex)
= P(Both male OR both female)
= P(Both male) + P(Both female) (again mutually exclusive)
= P(1st is male AND 2nd is male) + P(1st is female AND 2nd is female)
= P(1st is male)P(2nd is male|1st is male) + P(1st is female)P(2nd is female|1st is female) again using the general multiplication rule.
= (10/15)(9/14) + (5/15)(4/14)
= 11/21

iii)

P(Same litter and same sex)
= P(both male from first litter OR both male from second litter OR both female from first litter OR both female from second litter)
= P(both male from first litter) + P(both male from second litter) + P(both female from first litter) + P(both female from second litter)
= (4/15)(3/14) + (6/15)(5/14) + (3/15)(2/14) + (2/15)(1/14)
= 5/21
(If you would like me to write out the step with the general multiplication rule, let me know.)

iv)

P(same litter | same sex)
= P(same litter AND same sex)/P(same sex) from the definition of conditional probability. The probability in the numerator can be obtained from part iii) and the denominator can be obtained from part ii).
= {(4/15)(3/14) + (6/15)(5/14) + (3/15)(2/14) + (2/15)(1/14)}/{(10/15)(9/14) + (5/15)(5/14)}
= (5/21)/(11/21)
= 5/11

Answer 2

I erred.