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:

$\displaystyle P(X = 113) = 0.321201074564791$

Using the formula if you've got it right you should get the same value for $\displaystyle b(x; n, P)$

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.

$\displaystyle 195 * 0.3212 = 62.634$

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.

-Matthew