How to calculate reliabilty of humans in data-entry tasks? Please help me reason about this:

I have many, simple, data-entry tasks to be executed by humans. Of course they will make mistakes, so the result will be wrong sometimes.

I don't know, before hand, how often a human will make a mistake, but let's assume a person will make a mistake 10% of the times.

If I now let two different persons solve the same task, their results should match. If the results do not match, I could let a third person solve the task and thus find the right answer.

There is also the case where two persons make the same mistake on the same task, giving a wrong but mathcing answer, thus not detecting the failure.

My question is:
How can I calculate the probabilities of an error happening?  

Given the answer above, I could then calculate the amount of safety I could get by having 3 or 4 different persons solving the same task.

Thanks a lot!
You need to have a model of the errors, which will depend on the task.  The simplest is where the task is to enter $n$ binary choices, so on each choice there is only one possible error.  Let $p$ be the chance that a single bit is entered incorrectly.  The chance that a given task is completed correctly is then $(1-p)^n$, which corresponds to $90\%$ in your guess.  If you have two people do the same task, the chance they both make a mistake is $0.10^2=0.01=1\%$, but the chance they make an error on the same bit is much smaller.  

As the chance of one error is fairly small, there is not much wrong in assuming that nobody makes more than one error.  This lets us say $np=0.10, p=\frac {0.10}n$  Then the chance that two people make the same error is $np^2=\frac {0.01}n$.  The factor $\frac 1n$ comes from the fact that the errors have to match.  

If the data is more complicated, like entering names, there are many different errors that can be made, so the chance of matching errors is much lower.  There are probably particular errors that become rather common, however.  If somebody's last name is Jons, you will probably have a relatively high chance it will be entered as Jones.  This is much harder to model.
Since each person works independently, the event "person $1$ makes a mistake performing task $i$" is independent from the event "person $2$ makes a mistake performing task $i$", meaning that the probability of both people making an error for task $i$ is $0.1\cdot 0.1 = 0.01$. This means that if you have $100$ tasks, the average number of errors you can expect (the expected value is $1$.