GATE EE 2022 Set 1 — Question 5
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General Aptitude → Quantitative Aptitude → Elementary Statistics & Probability
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Question
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?
Correct answer
(C) (2)/(3)
Solution
Let be the pattern on the front view and be the pattern on the rear view. A flip around an axis in the plane of the disc results in a new front view and a new rear view , where is the reflection operator across axis . The disc retains the same views if and .From the figure:
- Front View (): Top-left and bottom-right are horizontal lines (); top-right and bottom-left are solid grey ().
- Rear View (): Top-left and bottom-right are solid grey (); top-right and bottom-left are horizontal lines ().
1.Axis 1-1 (Vertical): and . Thus, and . The views are retained.
2.Axis 2-2 (Diagonal): swaps top-left and bottom-right. Since has in both positions, . Since has in both positions, . Thus, . The views are NOT retained.
3.Axis 3-3 (Diagonal): swaps top-right and bottom-left. Since has in both positions, . Since has in both positions, . Thus, . The views are NOT retained.
Out of the 3 equally likely axes, the views are not retained for 2 axes (2-2 and 3-3). Therefore, the probability is .Continue learning with Success Tracker
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