Let x equal the number of typos on a printed page with a mean of 4 typos per page.

(a) what is the probability that a randomly selected page has at least one typo on it?
(b) what is the probability that a randomly selected page has at most one typo on it?

a) There is a 98.17% probability that a randomly selected page has at least one typo on it.

b) There is a 9.16% probability that a randomly selected page has at most one typo on it.

Step-by-step explanation:

Since we only have the mean, we can solve this problem by a Poisson distribution.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

In this problem, we have that

(a) What is the probability that a randomly selected page has at least one typo on it?

Thats is . Either a number is greater or equal than 1, or it is lesser. The sum of the probabilities must be decimal 1. So:

In which

.

So

There is a 98.17% probability that a randomly selected page has at least one typo on it.

(b) What is the probability that a randomly selected page has at most one typo on it?

This is . So:

There is a 9.16% probability that a randomly selected page has at most one typo on it.

25% is the answer