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, 2, or 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? A. 0 B. 1/3 C. 2/3 D. 1
GATE 2022 · General Aptitude · Probability · medium
Answer: P(disc does NOT retain same views) = 2/3
- Identify which flips preserve the disc's view: The disc's shading pattern is symmetric about exactly one of the three axes (axis 3, the diagonal). Flipping about axis 3 maps the pattern onto itself: view unchanged. Flipping about axis 1 or axis 2 does NOT reproduce the same shaded regions: view changes. So P(view retained) = 1/3.
- Apply complementary probability: P(does NOT retain) = 1 - P(retains) = 1 - 1/3 = 2/3