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 86 筆
第 21 頁
... probability of 1. " The probability of an impossible event is 0 ; thus the probability that a 100 will turn up when a die is thrown is 0 . Very often we want to determine the probability that the result of an experiment is in a given ...
... probability of 1. " The probability of an impossible event is 0 ; thus the probability that a 100 will turn up when a die is thrown is 0 . Very often we want to determine the probability that the result of an experiment is in a given ...
第 23 頁
... probability that the number on the first bicycle one encounters will not have any 8's among its digits ? 65a . Six ... probability that they will spell out the word " DEAF ” ? b . The same process is performed on a set of cards ...
... probability that the number on the first bicycle one encounters will not have any 8's among its digits ? 65a . Six ... probability that they will spell out the word " DEAF ” ? b . The same process is performed on a set of cards ...
第 153 頁
... probability of missing with all three shots is 1/2 49/144 , and so the solution to the problem is 1-49 / 144 = 7 / 9-7 / 8 = 95 / 144≈ 0.66 . 77. We will solve the problem in the formulation given in the remark . Let us suppose ...
... probability of missing with all three shots is 1/2 49/144 , and so the solution to the problem is 1-49 / 144 = 7 / 9-7 / 8 = 95 / 144≈ 0.66 . 77. We will solve the problem in the formulation given in the remark . Let us suppose ...
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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 given Hence inclusion and exclusion intersection k-gons knights length mathematical induction maximum number multiple 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