GATE 2022 EE – Question 5
The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or 3-3 chosen uniformly at random.
What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?
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Correct answer: (C) $\frac23$
Explanation
Flipping about axis 1-1 (the vertical axis) brings the rear pattern forward exactly as it is drawn, and the front pattern to the back, so both views are retained. Flipping about axis 2-2 or 3-3 moves the vertically hatched wedge and the horizontally hatched wedges to positions where the original pattern does not have them, so the views change. Hence the probability is $\frac23$.