Probability of Error Occurring in Message

[bob78h]

We are given a message of length n (it has n characters). There is a 0.1 probability for each character to be corrupted. What is the probability that m characters are corrupted?


I honestly have no idea how to solve this. Suppose you have 7 characters and you want to know the probability that 2 are corrupted. There is a 21 possible combinations of 2. Each character has a .1 probability of corruption so do 2 characters have a .2 probability? Or a .1*.1 probability? Once I know the probability of 2 being corrupted, do I multiply by the 21 combinations of 2?

Thanks for any help you guys can provide.

 

[mathman]

Use the binomial distribution. (n!/{m!(n-m)!})p^mq^n-m, where p = 0.1 and q = 1-p.