For the range 1 to 210 for n:

additional proportions: (check these for larger primorials)

8/35 numbers have zero prime factors from 2,3,5,7:
0000 occurs 48/210=8/35 of the time, so 8/35 of numbers don't have any of prime factors 2 or 3 or 5 or 7.

46/105=8/35+4/35+2/35+4/105 numbers have one prime factor from 2,3,5,7:
1000 occurs 48/210=8/35 of the time, so 8/35 of numbers have prime factor 2 and don't have any of prime factors 3 or 5 or 7.
0100 occurs 24/210=4/35 of the time, so 4/35 of numbers have prime factor 3 and don't have any of prime factors 2 or 5 or 7.
0010 occurs 12/210=2/35 of the time, so 2/35 of numbers have prime factor 5 and don't have any of prime factors 2 or 3 or 7.
0001 occurs 8/210=4/105 of the time, so 4/105 of numbers have prime factor 7 and don't have any of prime factors 2 or 3 or 5.

4/15=4/35+2/35+4/105+1/35+2/105+1/105 numbers have two prime factors from 2,3,5,7:
1100 occurs 24/210=4/35 of the time, so 4/35 of numbers have prime factor 2 and 3 and don't have either of prime factors 5 or 7.
1010 occurs 12/210=2/35 of the time, so 2/35 of numbers have prime factor 2 and 5 and don't have either of prime factors 3 or 7.
1001 occurs 8/210=4/105 of the time, so 4/105 of numbers have prime factor 2 and 7 and don't have either of prime factors 3 or 5.
0110 occurs 6/210=1/35 of the time, so 1/35 of numbers have prime factor 3 and 5 and don't have either of prime factors 2 or 7.
0101 occurs 4/210=2/105 of the time, so 2/105 of numbers have prime factor 3 and 7 and don't have either of prime factors 2 or 5.
0011 occurs 2/210=1/105 of the time, so 1/105 of numbers have prime factor 5 and 7 and don't have either of prime factors 2 or 3.

13/210=1/35+2/105+1/105+1/210 numbers have three prime factors from 2,3,5,7:
1110 occurs 6/210=1/35 of the time, so 1/35 of numbers have prime factor 2 and 3 and 5 and don't have prime factor 7.
1101 occurs 4/210=2/105 of the time, so 2/105 of numbers have prime factor 2 and 3 and 7 and don't have prime factor 5.
1011 occurs 2/210=1/105 of the time, so 1/105 of numbers have prime factor 2 and 5 and 7 and don't have prime factor 3.
0111 occurs 1/210 of the time, so 1/210 of numbers have prime factor 3 and 5 and 7 and don't have prime factor 2.

1/210 numbers have four prime factors from 2,3,5,7:
1111 occurs 1/210 of the time, so 1/210 of numbers have prime factor 2 and 3 and 5 and 7.

8/35+46/105+4/15+13/210+1/210=1
Accumulate[{8/35, 46/105, 4/15, 13/210, 1/210}]
output: {8/35,2/3,14/15,209/210,1}


A024451/A002110
247/210 = (8/35)*0 + (46/105)*1 + (4/15)*2 + (13/210)*3 + (1/210)*4 = 1/2 + 1/3 + 1/5 + 1/7
without reduced fractions:
247/210 = (48/210)*0 + (92/210)*1 + (56/210)*2 + (13/210)*3 + (1/210)*4 = 1/2 + 1/3 + 1/5 + 1/7
This gives the average number of distinct prime factors <= prime(n)=7 in the natural numbers up to 2*3*5*7=210


Mathematica code for some other abcde solutions

Python code for some other abcde solutions