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Chapter 2: Q. 2.39 (page 51)
There are hotels in a certain town. If people check
into hotels in a day, what is the probability that they each check into a different hotel? What assumptions are you making?
the probability that they each check into a different hotel is0.48.
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An instructor gives her class a set of problems with the information that the final exam will consist of a random selection of them. If a student has figured out how to do the problems, what is the probability that he or she will answer correctly
all problems?
at leastof the problems?
Consider Example, which is concerned with the number of runs of wins obtained whenwins and losses are randomly permuted. Now consider the total number of runs鈥攖hat is, win runs plus loss runs鈥攁nd show that
Consider the matching problem, Example, and define it to be the number of ways in which themen can select their hats so that no man selects his own.
Argue that. This formula, along with the boundary conditions, can then be solved for, and the desired probability of no matches would be
Hint: After the first man selects a hat that is not his own, there remain men to select among a set of hats that do not contain the hat of one of these men. Thus, there is one extra man and one extra hat. Argue that we can get no matches either with the extra man selecting the extra hat or with the extra man not selecting the extra hat.
A forest containselk, which are captured, tagged, and then released. A certain time later,the elk are captured. What is the probability that these have been tagged? What assumptions are you making?
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The
classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class, and 16 in the German class. There are 12 students who are in both Spanish and French, 4 who are in both Spanish and German, and 6 who are in both French and German. In addition, there are 2 students taking all 3 classes.
(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?
(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
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