Problem 18
In a fierce battle, not less than \(70 \%\) of the soldiers lost one eye, not less than \(75 \%\) lost one ear, not less than \(80 \%\) lost one hand, and not less than \(85 \%\) lost one leg. What is the smallest percentage who could have lost simultaneously one car, one eye, one hand, and one leg? This problem comes from Tangled Tales by Lewis Carroll, the author of Alice in Wonderland.
Problem 19
The waiting room of a dentist's office contains a stack of 10 old magazines. During the course of a morning, four patients, who are waiting during non- overlapping times, select a magazine at random to read. Calculate in two ways the probability that two or more patients select the same magazine.
Problem 20
What is the probability that in a group of 10 people, at least 2 have the same birthday? Assume that nobody was born on February 29 th. Use a calculator to get a good. approximate answer.
Problem 22
Recall that by definition, a discrete sample space may contain a countably infinite number of outcomes. This exercise gives an example of such a countably infinite sample space. Suppose we flip a fair coin until it comes up heads. Of course, there is no way to know in advance how many flips will be required. Design a sample space and a probability density to model this situation. Prove that the probability density you define is legitimate.
