Mathematical Questions and Solutions Volume 31
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Mathematical Questions and Solutions Volume 31

Mathematical Questions and Solutions Volume 31


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1879 Excerpt: ...may, however, with equal propriety, be taken as terminated at the points D, E in the opposite sides of the triangle; and in this form the problem has been reproposed for solution as Question 5885. 5853. (By Professor Crofton, F.R.S.)--Explain the following paradox: --One bag (A) contains 5 cheques, whereof 2 are known to be over 5 and 3 under. Another hag (B) contains 7 cheques, 4 over 5 and 3 under. Find the chance, if a cheque be drawn from A, that it exceeds in amount one drawn from B. There are 35 cases, all equally probable; 6 evidently favourable, 12 unfavourable, and 17 doubtful. In these 17 cases, as all we know is that the 2 cheques drawn are both over o, or both under, it is an even chance that one exceeds the other. Hence the chance required, that the cheque from A exceeds that from B, is-fir t = f . But the chance that the cheque from A exceeds 5 is = fJ;, so that there is a less chance that the cheque drawn from A exceeds 5 than that it exceeds an (unknown) quantity which is likely to be greater than 5; the odds being i to 3. A priori, one would say it must be the other way. Solution by W. J. Macdonald, M.A. Though the chance that a cheque from A exceeds one from B is f, yet the chance that the latter exceeds 5 is only f; therefore the chance that a cheque from A exceeds a quantity greater than 5 is only f g x f =- z. 5831. (By Professor Minchin, M.A.)--If S and E be a conic and its evolute, and if X be the conic whose intersections with S are the feet of the normals drawn to S from a point P: prove that (1) the perpendicular from P on its polar with respect to S is a tangent to X at P; (2) the centre of gravity of the feet of the four normals is the middle point of th...


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Product Details
  • ISBN-13: 9781232241850
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 32
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1232241857
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 77 gr


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