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In many of the examples in 2, it is easy to determine the number of outcomes in each event. In more complicated examples, determining the number of outcomes that comprise the sample space (or an event) becomes more dif cult. To associate probabilities with events, it is important to know the number of outcomes both in an event and in the sample space. Some simple rules can be used to simplify the calculations. In Example 2-4, an automobile manufacturer provides vehicles equipped with selected options. Each vehicle is ordered With or without an automatic transmission With or without air conditioning With one of three choices of a stereo system With one of four exterior colors The tree diagram in Fig. 2-6 describes the sample space of all possible vehicle types. The size of the sample space equals the number of branches in the last level of the tree and this quantity equals 2 2 3 4 = 48. This leads to the following useful result.

In the preceding snippet, you used match() to extract the captured group. However, the behavior of match() can be tricky here. When the expression passed to match() has the global ag set, match() returns an array of all the substrings that match the pattern. It does not give you any of the captures. You ll read more on the global ag in the section Regular Expression Flags. When you use match() with an expression that does not have the global ag set, it returns an array containing the rst matching substring, followed by all the capture groups in the expression for that match. This is the case in the preceding snippet. The expression does not have the global ag set, and match() returns an array where the rst entry is the matching substring "New York: 212-555-2499". The second entry (matches[1]) is the part of the expression that was captured, "212-555-2499". Because of this tricky difference, if you need to use capture groups, you might do well to stick to the by-now familiar function I revisit in the following section.

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Multiplication Rule (for counting techniques)

Let s modify this program using RegExp s exec() method so that you can get both the names and the numbers for every of ce in the list in one fell swoop. You ll add them to an associative array so you can look up numbers such as contacts["New York"]. In Example 12-4, you re parsing arbitrary text with a speci c format into a data structure that you can conveniently use in other code. That s pretty useful!

and the GUI and should be modified if new types of messages or new information for existing message types is to be communicated. The GUI process parses the received GUIMessage and, depending on the type of the message received, responds in one of many ways such as adding the message to the

If an operation can be described as a sequence of k steps, and if the number of ways of completing step 1 is n1, and if the number of ways of completing step 2 is n2 for each way of completing step 1, and if the number of ways of completing step 3 is n3 for each way of completing step 2, and so forth, the total number of ways of completing the operation is n1 n2 p nk

var contacts:Object = new Object(); var contactText:String = "Call us at one of these numbers.\n" + "Los Angeles: 310-555-2910\n" + "New York: 212-555-2499\n" + "Boston: 617-555-7141";

EXAMPLE S2-1

In the design of a casing for a gear housing, we can use four different types of fasteners, three different bolt lengths, and three different bolt locations. From the multiplication rule, 4 3 3 36 different designs are possible. Permutations Another useful calculation is the number of ordered sequences of the elements of a set. Consider a set of elements, such as S {a, b, c}. A permutation of the elements is an ordered sequence of the elements. For example, abc, acb, bac, bca, cab, and cba are all of the permutations of the elements of S.

var officeAndPhone:RegExp = /^([\w\s]+): (\d{3}-\d{3}-\d{4})/gm; var result:Object; while (result = officeAndPhone.exec(contactText)) { contacts[result[1]] = result[2]; } trace(contacts["New York"]); //212-555-2499 trace(contacts["Boston"]); //617-555-7141

The number of permutations of n different elements is n! where n! n 1n 12 1n 22 p 2 1 (S2-1)

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