If the children are Alan (=0.5) and Barb (=0.3):
this means: not Alan = 0.5 and not Barb = 0.7:
a) both Alan and Barb: 0.5 and 0.3 = 0.5 x 0.3 = 0.15
b) exactly one: either Alan and not Barb or not Alan and Barb
= 0.5 x 0.7 + 0.5 x 0.3 = 0.35 + 0.15 = 0.50
c) neither one: not Alan and not Barb = 0.5 x 0.7 = 0.35
d) at least one: both Alan and Barb or Alan and not Barb or not Alan and Barb
= 0.5 x 0.3 + 0.5 x 0.7 + 0.5 x 0.3 = 0.15 + 0.35 + 0.15 = 0.65
With "and", you multiply; with "or", you add.