Probability - Quant/Math -
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Question 4 the day: October 25, 2002
The question for the day is from the topic of Probability.

Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?

(1)

1 / 18

(2)

64 / 4032

(3)

63 / 64

(4)

1 / 9

Solution:

The number of ways of choosing the first square is 64. The number of ways of choosing the second square is 63. There are a total of 64 * 63 = 4032 ways of choosing two squares.

If the first square happens to be any of the four corner ones, the second square can be chosen in 2 ways. If the first square happens to be any of the 24 squares on the side of the chess board, the second square can be chosen in 3 ways. If the first square happens to be any of the 36 remaining squares, the second square can be chosen in 4 ways. Hence the desired number of combinations = (4 * 2) + (24 * 3) + (36 * 4) = 224. Therefore, the required probability = .