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Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?Answer VerifiedHint: You can observe in a chessboard that there are types of squares when we are looking for common sides. The first type is with 4 adjacent squares, the second is with 3 and the third is with 4 adjacent squares. Find the probability that two squares have a common side each type and add. Complete step-by-step answer: We know there are 64 squares in a chess board alternatively in black and white. We have to select a square at random. We observe that there are three types of square with respect to adjacency in the chess board.\[\] Note: The key to solving this question is distinguishing the different types of squares. It is also to be noted that the selection of three different types of square is mutually exclusive and that is the reason we could add the probabilities. No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! Solution The correct option is C118The explanation for the correct answer.Solve for the required probability.Out of 64 squares, two squares are selected =C264 ways =32x63 waysNumber of ways of selecting the pairs which have the common side =12Favorable cases =4(2)+24(3)+36(4)=112(As each corner has two neighbors, every 24squares on the border have 3neighbors, and the remaining 36 squares have four neighbors)Hence, the required probability =11232 ×63=118Hence, option(C) is the correct answer.Textbooks Question Papers Home What is the probability that 2 squares chosen at random from a chess board have just 1 corner in common?Required probability = = 0.048.
What is the probability that two squares smallest dimension selected randomly from a chessboard will have only one common corner?In this case, there's a 4/64 chance of obtaining both squares with one corner common.
What is the probability that two squares selected randomly from a chess board?The total numbers of such square is 24. So probability of selecting second type of square is 2464. We see that after selection of one second type square the number squares left are 63. So the probability of selecting an adjacent square for the selected second type is 363.
How many 2x2 squares are there in a chess board?Using what we have worked out so far we can now calculate the total number of squares on the chessboard: Number of 1x1 squares = 8 x 8 = 64. Number of 2x2 squares = 7 x 7 = 49. Number of 3x3 squares = 6 x 6 = 36.
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