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How many do they have if they must answer at least three out of the first five? Solution Clearly, we are sampling without replacement and the order is irrelevant. For the first part, we have number of choices = 10 = 120. 7 For the second part, we have three possibilities: we can answer three out of the first five and four out of the second five or four out of the first five and three out of the second five or five out of the first five and two out of the second five. 4(iii), we have number of choices = 5 3 5 5 + 4 4 5 5 + 3 5 5 = 110.

We begin by contemplating some of the ways in which chance enters our lives. Consider the following statements: (S1) There is a one in two chance that this coin will come up tails. (S2) There’s a strong chance that Wales will beat Denmark in the match tonight. 56. Each of these statements manifests a different way in which chance is used in everyday language. We will examine each of them in turn. 1 Probability by symmetry Consider a fair coin which we know to have no defects. Apart from the fact that one side is a head and the other a tail, there are no other features which distinguish one side from the other.

T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, 1920). 1 The concept of a set A set is simply a list of symbols. Usually, each symbol in the set is the name of an object, which may be conceptual in origin or which may have a physical existence. The members or elements of such a set are usually displayed within braces { } and separated by commas. For example, in later chapters we will be much concerned with dice games where the set of interest will contain the possible numbers which can appear on the faces of a dice.

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50 Jahre Deutsche Statistische Gesellschaft Tagungen 1961 und 1962


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