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
Describe each view in the front viewer's coordinates, with axis 1-1 vertical and the horizontal dashed line as reference.Front view (front face):
- a vertically hatched sector in the upper-left, between the horizontal line and axis 3 ( to );
- a horizontally hatched sector in the upper-right, between the horizontal line and axis 2 ( to );
- a horizontally hatched sector at the bottom, between the lower ends of axes 2 and 3 ( to ).
1.Axis 1-1 (vertical): reflecting in the vertical axis undoes the left-right mirror. The back face then shows vertical hatching at upper-left, horizontal hatching at upper-right and the bottom sector, which is exactly the original front view. By the same argument the new rear view equals the old rear view. The views are retained.
2.Axis 2-2 (the line): the reflection maps an angle to and turns vertical hatching into horizontal hatching. The back face's upper-right sector ( to ) moves to to , and its upper-left sector moves to to . A sector now sits right next to axis 1 at the top, which the original front view does not have, so the views are not retained.
3.Axis 3-3 (the line): by the same reasoning the shaded sectors end up in different positions from the original front view. The views are not retained.
The views change for 2 of the 3 equally likely axes, soContinue learning with Success Tracker
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