A novel bacterial defense system against invading viruses, known as Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR), has recently been described. Unlike other bacterial defense systems, CRISPRs, are virus-specific and heritable, producing a form of adaptive immune memory. Specific bacterial DNA regions, CRISPR loci, incorporate on average 25 copies of unique short (30 base pair) regions of viral DNA which allow the bacteria to detect, degrade and have immunity against viruses with matching sub-sequences. Ideally, the number of unique viral-copied regions a CRISPR loci contains would grow indefinitely to allow immunity to accumulate to a large number of viruses. However, the number of these viral-copied regions in the CRISPR loci of any bacteria is limited in length and number. We use a birth-death master equation model to explore the growth and decay of the length of the CRISPR loci and thus the number of viral-copied regions. Additionally, we use a simple probabilistic model to determine bounds on the length of viral-copied region within the CRISPR locus.