Final answer:
The probability of no error in 20 million divisions made by the Pentium chip, with an error rate of 1 in 9 billion, is calculated by raising the single division success probability (8,999,999,999/9,000,000,000) to the power of 20 million. This is a very high probability, indicating almost certainty of no error.
Step-by-step explanation:
The question asks for the probability of no error occurring when a computer performs 20 million division problems, given that the Pentium chip in question has a probability of a division error in 1 out of 9 billion cases. We can model this situation using the concept of binomial probability, where each division is a trial with two possible outcomes: success (no error) or failure (an error).
Since the probability of an error is 1 in 9 billion, the probability of no error (success) for a single division is 1 minus (1/9,000,000,000) = 8,999,999,999/9,000,000,000. To find the probability of no errors in 20 million divisions, we raise the single-division success probability to the power of 20 million:
P(no error in 20 million divisions) = (8,999,999,999/9,000,000,000)^{20,000,000}
This calculation would typically require a computer or a calculator capable of handling very large exponents. As this is an example of a very unlikely event (similar to the chances of winning a large lottery), the actual probability is very close to 1, indicating that it's almost certain there will be no error in any given 20 million divisions.