Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. A newspaper finds that the mean number of typographical errors per page is eight. Find the probability that (a) exactly five typographical errors are found on a page, (b) at most five typographical errors are found on a page, and (c) more than five typographical errors are found on a page. (a) $P$ (exactly five typographical errors are found on a page) = (Round to four decimal places as needed.)

Step 1 ：The problem involves finding the probability of a certain number of events (typographical errors) happening in a fixed interval (a page). This is a classic example of a problem that can be solved using the Poisson distribution. The Poisson distribution is used to model the number of events happening in a fixed interval of time or space.

Step 2 ：The formula for the Poisson distribution is: \(P(X=k) = \frac{λ^k * e^{-λ}}{k!}\) where: \(P(X=k)\) is the probability of k events happening in an interval, λ is the average rate of value (mean number of events per interval), e is the base of the natural logarithm (approximately equal to 2.71828), k! is the factorial of k.

Step 3 ：In this case, λ is 8 (the mean number of typographical errors per page), and we want to find \(P(X=5)\), the probability of exactly 5 typographical errors on a page.

Step 4 ：Substitute the given values into the formula: \(P(X=5) = \frac{8^5 * e^{-8}}{5!}\)

Step 5 ：Solve the equation to get the final answer.

Step 6 ：Final Answer: The probability that exactly five typographical errors are found on a page is approximately \(\boxed{0.0916}\).