Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theoryHolden-Day, 1964 |
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第 1 到 3 筆結果,共 36 筆
第 6 頁
... denote by A U B ( read “ A union B❞ or " A cup B ” ) the set of all elements in A or B ( or both ) . We call A U B the union or sum of A and B. In fig . 1 , where A and B are represented by two 66 A B Fig . 1 discs , A U B is the ...
... denote by A U B ( read “ A union B❞ or " A cup B ” ) the set of all elements in A or B ( or both ) . We call A U B the union or sum of A and B. In fig . 1 , where A and B are represented by two 66 A B Fig . 1 discs , A U B is the ...
第 21 頁
... denote the number of times that E occurred , and define Pr { E } to be the limit of nÅ / n as n becomes indefinitely large . In the above example where E = { 2,4,6 } we have Pr { E } = } . Let E , and E2 be two events and denote by E ...
... denote the number of times that E occurred , and define Pr { E } to be the limit of nÅ / n as n becomes indefinitely large . In the above example where E = { 2,4,6 } we have Pr { E } = } . Let E , and E2 be two events and denote by E ...
第 22 頁
... denote by EF ( read " E and F " ) the event consisting of all outcomes which are in both E and F. For example , in the experiment of throwing a die , if E = { 1,2,4,6 } and F = { 2,3,5,6 } , then EOF = { 2,6 } . In the case where Pr { F } ...
... denote by EF ( read " E and F " ) the event consisting of all outcomes which are in both E and F. For example , in the experiment of throwing a die , if E = { 1,2,4,6 } and F = { 2,3,5,6 } , then EOF = { 2,6 } . In the case where Pr { F } ...
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A₁ A₂ An+m arrangements b₁ B₂ binomial coefficients binomial theorem bishops black squares C₁ chessboard chord circle coefficient color column compute the number Consequently consider corresponding customers denote determine the number diagonals digits dihedral angle divided divisible draw equally likely possible equation equidistant equivalence classes exactly example experiment favorable outcomes follows formula G₁ given Hence inclusion and exclusion intersection k-gons knights length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks S₁ segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices