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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A system is composed of components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector , where is equal to if component is working and is equal to if component is failed.
(a) How many outcomes are in the sample space of this experiment?
(b) Suppose that the system will work if components and are both working, or if components and are both working, or if components , , and are all working. Let W be the event that the system will work. Specify all the outcomes in W.
(c) Let be the event that components and are both failed. How many outcomes are contained in the event ?
(d) Write out all the outcomes in the event .
The chess clubs of two schools consist of, respectively, players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that
(a) Rebecca and Elise will be paired?
(b) Rebecca and Elise will be chosen to represent their schools but will not play each other?
(c) either Rebecca or Elise will be chosen to represent her school?
A, B, and C take turns flipping a coin. The first one to get a head wins. The sample space of this experiment can be defined by
(a) Interpret the sample space.
(b) Define the following events in terms of S:
(i) wins = .
(ii) wins = .
(iii) .
Assume that A flips first, then B, then C, then A, and so on.
A woman has keys, of which one will open her door.
(a) If she tries the keys at random, discarding those that do not work, what is the probability that she will open the door on her kth try?
(b) What if she does not discard previously tried keys?
If there are strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?
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