A company that translates books between various languages is currently testing a​ computer-based translation service. The founder of the company expects the computer program to make some​ errors, but then so do human translators. The computer error rate is supposed to be an average of 2 per 500 words of translation. Suppose the company founder randomly selects a ​3,000-word passage. Assume that the Poisson distribution applies and that the computer error rate is actually 2 errors per 500 words. Complete parts a through c.
a. Determine the probability that no errors will be found.
The probability is ___. Round to four decimal places as​ needed.)

b. Calculate the probability that more than 30 errors will be found.
The probability is ___. ​(Round to four decimal places as​ needed.)

c. Find the probability that fewer than 15 errors will be found.
The probability is ___. ​(Round to four decimal places as​ needed.)