A painter draws 64 equal squares of 1 square inch on a square canvas measuring 64 square inches. She chooses two squares (1 square inch each) randomly and then paints them. What is the probability that two painted squares have a common side?
- 112/2016
- 1/3
- 512/10034
- 3/97
- 7/108
The Correct Option is A
Solution and Explanation
Total number of selections = 64C2 = 64 x 63/2 = 2016
In each row, there will be seven pairs of squares that share a common side.
Thus, a total of 7x8 = 56 pairs in all the rows.
Similarly, in each column, there will be seven pairs of squares that share a common side. Thus, a total of 7x8 = 56 pairs in all the columns.
Thus, the required probability = 56 + 56/2016 = 112/2016.
Hence, option A is the correct answer.
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