Squares Having a Common SideDate: 03/08/99 at 08:57:27 From: suresh kumar Subject: Probability In choosing two squares from a chess board, what is the probability that they have a common side? Date: 03/08/99 at 16:25:11 From: Doctor Anthony Subject: Re: Probability There are 3 types of square: (a) squares in the middle part that have 4 squares with common borders (b) corner squares (of which there are 4) that have 2 squares with a common border (c) edge squares, which have 3 squares with a common border There are 36 type (a) squares. 4 type (b) squares. 24 type (c) squares. Altogether there are 64 squares on the board. The probability that two squares have a common border is then: Prob(type a) x 4/63 + Prob(type b) x 2/63 + Prob(type c) x 3/63 = 36/64 x 4/63 + 4/64 x 2/63 + 24/64 x 3/63 36 x 4 + 4 x 2 + 24 x 3 224 1 = ------------------------- = ------ = ---- 64 x 63 4032 18 - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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