If size of every box of chess board is 1*1, then what will be the probability to get a square of siz

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01 Mar 2012 chess board

If size of every box of chess board is 1*1, then what will be the probability to get a square of size 4*4, if we have to choose a square of any size in the chess board of size 8*8.

OPtion

1) 25/204
2) 25/194
3) 4/51
4) 8/97
5) 3/68
6) 9/194
7) 3/8
8) 2/5
9) 16/125
10) none of these

Solution

total squares of size 4*4 = 5*5 = 25
total squares = 1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*6 + 7*7 + 8*8 = 204
so probability = 25/204

Correct Option: 1 Best Solution (9)

Dr.Dipin Singh   12 years AGO

Total 204v squares are availabie in 8*8 square chess board.

No of squares of different sizes are


1, 8x8 square
4, 7x7 squares
9, 6x6 squares
16, 5x5 squares
25, 4x4 squares
36, 3x3 squares
49, 2x2 squares
64, 1x1 square

So probability of getting 4*4 square = 25/204 .. option 1

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Suresh Varma P   12 years AGO

No. of Squares with 1x1 = 8 * 8 = 64
No. of Squares with 2x2 = 7 * 7 = 49
No. of Squares with 3x3 = 6 * 6 = 36
No. of Squares with 4x4 = 5 * 5 = 25
No. of Squares with 5x5 = 4 * 4 = 16
No. of Squares with 6x6 = 3 * 3 = 9
No. of Squares with 7x7 = 2 * 2 = 4
No. of Squares with 8x8 = 1 * 1 = 1

Total no. of squares = 64+49+36+25+16+9+4+1 = 204

Probability of getting a square of size 4*4 = 25/204

Ans: option 1

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praveen   12 years AGO

4*4 squares will be 25 ,5 in horizontal and 5 in vertical,similarly total squares will be 204,64+49+36+25+16+9+4+1

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Maya Krishnamurthy   12 years AGO

25/204 count no of 4*4 squares..which comes to 25.
204 the no os ANY size square in the chess board.
1*1 =64
2*2 =49
3*3 =36
4*4 =25
5*5 =16
6*6 =9
7*7 =4
8*8 =1
all are squares in reverse order.
so the answer is option 1)25/204.

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Suresh K   12 years AGO

Total number of squares = 204
Total number of 4*4 squares = 25
Required probability = 25/204

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Tijo Jose   12 years AGO

Total number of squares in an 8x8 chessboard is 204! That includes all 1x1, 2x2, 3x3, ..., 8x8 squares...

Now, there are 25 4x4 squares!

So, probability = 25 / 204

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sridhar reddy   12 years AGO

(4+1)^2 =25chances of 4x4 squares
out of 1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2=204
it's probability is 25/204

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Balakrishnan M   12 years AGO

There are 204 squares of all sizes in a standard 8*8 chessboard.i.e.,1*1 is 64, 2*2 is 49,3*3 is 36,4*4 is 25,5*5 is 16, 6*6 is 9,7*7 is 4, 8*8 is 1. probability to get a square of size 4*4=25/204

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Rakesh Kumar Kohli   12 years AGO

Number of squares of sizes 1*1,2*2,3*3,4*4, 5*5, 6*6,7*7,8*8 are 64,49,36,25,16,9,4 and 1 respectively.
Total number of squares that are formed =
64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204
Probability to get a square of size 4*4 = 25/204

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