When a man writes a letter (and fixes his mistakes), he notices that on average 1 character out of 1000 is incorrect, the man proceeds to write a letter with 6000 characters.

1. Let X be the number of errors left in the text what is the distribution of X, the expected value of E[X] and the variance var[X]?
2. What is the probability that the text is completely correct?
3. What is the most likely number of errors?
4. What is the probability that there will be at least 10 errors?