Solution of problem N1482 Poisson probability theory

Solution of problem N1482 Poisson probability theory

1482. A message of 2,000 characters is transmitted via the communication channel. The probability of distortion of each symbol when transmitting a message is 0.001. What is the probability that:
1) will there be 5 distorted symbols in the received message?
2) the message will be accepted correctly, if for this purpose the number of distorted symbols should not exceed 3?

Additional information:

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)