Answer:
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.