P = (good outcomes)/(total possible outcomes)
total outcomes = total number of possible pairs that can be made from 7 choices = (7*6)/(1*2) = 21
A good outcome is if we don't choose a sibling pair. Let's count how many siblings pairs we have:
If ABC are all siblings (AB, AC, BC), that gives us 3 siblings pairs that account for the 3 people that have 2 siblings each.
This leaves 2 other sibling pairs, DE and FG, which account for the 4 people that have 1 sibling each.
So we have 3+2=5 sibling pairs.
This means we have 21-5=16 pairs that are NOT made of siblings.
So P(not a sibling pair) = 16/21.
The correct answer is E.
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