A solution using Python:

```
import random
def random_dna_sequence(length):
return ''.join(random.choice('ACTG') for _ in range(length))
```

You want a DNA string with equal base probability. So the probability of each base appearing is `0.25`

. With the following function you can check how much each DNA string deviates from this predicted probability:

```
def base_frequency(dna):
d = {}
for base in 'ATCG':
d[base] = dna.count(base)/float(len(dna))
return d
for _ in range(20):
dna = random_dna_sequence(100)
print dna, base_frequency(dna)
```

which would generate a result like:

```
AAGTGACGCCCGGTGCGAAAAACACGCGCCTCTCCGTAGTCATTCAGACT {'A': 0.26, 'C': 0.32, 'T': 0.18, 'G': 0.24}
AAGGATCTACTACCTCGTCTATTTGAACTACTGTAGTGCTACTAACTCAT {'A': 0.28, 'C': 0.24, 'T': 0.34, 'G': 0.14}
TCCACTTCTTGGTCCTGAACACCTGCAATCACCTCTTACATCGTGCGACG {'A': 0.2, 'C': 0.36, 'T': 0.28, 'G': 0.16}
AATCTCCGGTGTGTCCGCTACGGAGGTTAGGGCACTCCGTGGGAAAGCTC {'A': 0.18, 'C': 0.26, 'T': 0.22, 'G': 0.34}
GCGTAGTTCGCATTGATTAACATAGTGGCGACCATAGACTTCTATTATCG {'A': 0.26, 'C': 0.2, 'T': 0.32, 'G': 0.22}
AAGTGAACCTGGACTGGGTGGATCGTCTCCCTCGTCCGGTCCTTGGTAGC {'A': 0.14, 'C': 0.28, 'T': 0.26, 'G': 0.32}
ATGACGATGACGATCATCGTCAACGCGCGTCGCGCACACTGCATATCCAA {'A': 0.28, 'C': 0.32, 'T': 0.18, 'G': 0.22}
GTGCATACCGGTGCGCGCGTGCGCTAGGTATTGGAATGCTACGCTTAACC {'A': 0.18, 'C': 0.26, 'T': 0.24, 'G': 0.32}
GCCCGCGTGCCGCCAAGGGATGGGGAGAGTATTTTCGCCCCCTAAGTGCC {'A': 0.16, 'C': 0.32, 'T': 0.18, 'G': 0.34}
TCAAGATTCTCCTAAATATATAATGATCATCCGTTGTCATTCTGCGGACT {'A': 0.28, 'C': 0.22, 'T': 0.36, 'G': 0.14}
TGTTTTAGCCCTGTAGCCGGACTACGAAGTTTTAGGCGCCCAGATTAAGG {'A': 0.22, 'C': 0.22, 'T': 0.28, 'G': 0.28}
AGACGAGCTTTCAAGTTCTTGAATCACTACCTTTGACGTCGAGTGTAAGG {'A': 0.26, 'C': 0.2, 'T': 0.3, 'G': 0.24}
TCGCATTGTAAATAGGAACCTGAAACCTGCCAAGGAGATACAGTCTAAAT {'A': 0.38, 'C': 0.2, 'T': 0.22, 'G': 0.2}
CATCCGTGTGGTAACAGTTAATGCCGGGCTCACCCTCAGGTGTGAAGGAT {'A': 0.22, 'C': 0.24, 'T': 0.24, 'G': 0.3}
ACCAAGACATACCTTAAGGCCCACGCGTACAAGTCACGCTCTCAATACGG {'A': 0.32, 'C': 0.34, 'T': 0.16, 'G': 0.18}
CGTCGTTGGTATTCAGAAAACGCTAGCACATATGGTGCCCAGTCAAAGGA {'A': 0.3, 'C': 0.22, 'T': 0.22, 'G': 0.26}
CGTCATTGCACCAAGTGTGGTACTTTGGGGACGTGAGGTAACAATCCCTG {'A': 0.22, 'C': 0.22, 'T': 0.26, 'G': 0.3}
TGGTCCCTGTTTCTCCATTCCGCGTCCATCGTGCGTTCGTCCTTTAAAGT {'A': 0.1, 'C': 0.32, 'T': 0.38, 'G': 0.2}
AATTCACTCTTTTAACGATGGAAACGGGCGTTTGTAGTGTGCCACTAACC {'A': 0.26, 'C': 0.22, 'T': 0.3, 'G': 0.22}
CCTTGTATACCCCACATGAAGAATGGGCCTGACATCAATAATCTTTAGAT {'A': 0.32, 'C': 0.24, 'T': 0.28, 'G': 0.16}
```