Question

find the probability that a rectangle selected at random from a chess board is a square​

Answer 1

Step-by-step explanation:

Total no. Of squares are :-

Square of size 1X1= 64=8^2 .

2X2 =49= 7^2

And so on. 8X8=1=. 1^2

So total squares using n(n+1)(2n+1)/6 where n=8

Total rectangles : we need to choose 2 out of 9 lines across ech dimension to make it a square, that is, 9c 2 .

So ans is ( 8*9*17/6 )/ 9c2 * 9c2 equals 17/108

Answer 2

Answer:

17/108

Step-by-step explanation:

Say the chess board is of 8 X 8.

Then, total number of squares is n(n+1)(2n+1)/6 where n is the side i.e. n = 8

=> total number of squares is n(n+1)(2n+1)/6 = (8 * 9 * 17 ) / 6 = 12 * 17

Total rectangles in 8X8 chessboard is (9C2)(9C2) = 36² .

So required probability is (12*17 )/ 36² = 17/(3 * 36) = 17/108