## Normalize probabilities

Hi everyone!

I am not sure if this question corresponds to this section, but here we go

I have a table of probabilities in the following way:

Dp a1 a2 a3 a4

453,2 0,75588 0,1474 0,0903 0,0418
523,3 0,72334 0,1372 0,0883 0,045
604,3 0,68883 0,1278 0,0854 0,0475
697,3 0,65272 0,1194 0,0821 0,0491
805,8 0,61545 0,1121 0,0789 0,05

So that for each diameter Dp, htere is a probability of having a1, a2, a3 and so on, and the sum of all these probabilities for each Dp is 1 (maybe in the expample this doesn´t occurs since I didn´t show all the values)

That is: a1(dp1) + a2(dp1) + a3(dp1) + a4(dp1) = 1
a1(dp2) + a2(dp2) + a3(dp2) + a4(dp2) = 1
......

But I need to know, form a mix of several diameters how many of them of each kind $a_i$ would be. For example, for a sample of diameters Dp1 and Dp2, where:
Dp1 + Dp2= N,
can I know from the previous percentajes how many of a1(Dp1) and a1(Dp2) would it be in the total?

but since a1(Dp1)+a1(Dp2) $!=$1 , then N1+N2 $!=$N