It is better to say "A child has only 50% chance
of inheriting each new mutation in their parents'
nucleus DNA". So if the parents have 10 new
!mutations between them, then the child receives
a random number out of those mutations, which is
most likely to be 5.
When you say "each child only has 50% chance of
inheriting any new mutations", that sounds like
a 50-50 chance of getting no inherited mutations.
That doesn't happen, because the process does
not "know" which nucleotides are mutations,
and which are Norm's.
My understanding is hazy but if I've got it right
that the inherited chromosome typically is read from
/both/ corresponding chromosomes from the parent
by taking a length from one or from the other, then
switching across, then as a subtlety, if /two/ mutations
are on the same chromosome of one parent and are
close together, then the expected "random" outcomes
are that you will most likely inherit both of them or
inherit neither of them; it is not "independent". This is
a deviation from the probabilities otherwise, where to
receive mutation A, or separate mutation B, or both of
A and B, or neither of them, are four equally likely
outcomes. Still, it is also not true to say that the random
event of receiving each mutation is always "independent".
It's "better" because it is closer to the actual expected
outcome.