Bioinformatician here (all be it a fairly new one).
To answer your question you can use binomial distribution. This page: Binomial Calculator has a calculator. And this page: Binomial Distribution has a little information on how binomial distribution is calculated. A Google search will pull up a lot more too.
To solve the problem we need to calculate the probability of there being a problem in 113 bases. You can use the formula in the second link or use the calculator in the first:
Probability your base pair is accurately sequenced (P)
Probability of success on a single trial: 0.99
Number of base pairs (n)
Number of trials: 113
For 0 failures
Number of successes (x): 113
Now if you've gone for the calculator option you want:
Using the formula if you've got it right you should get the same value for
So now we have the probability of a given trial containing no errors. Now it's a simple matter to multiply the probability by the 195 of sequences.
So of those 195 sequences on average approximately 63 will be correct and identical. There's also a good chance (well good enough to code for anyway) that there will be a couple more which are wrong and identical.
Hope this helps.