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?

Given:

There are two figures that represent the front and rear view of a disc.

Concept used:

Lines of symmetry are imaginary lines that pass through the center of the shape or object and divide it into identical halves.

Formula used:

Probability to does not retain same view = 1 - Probability to retain the same view

Calculation:

From the front and rear view of the disc, we conclude that the view is only symmetrical about 1-1 axis.

Therefore, the disc will retain the same front and rear views after the flipping operation after flipping about 1-1 axis out of three given axis.

∴ Probability to retain the same front and rear view of the disc = 1/3

∴ The probability that the disc DOES NOT retain the same front and rear views = 1 - 1/3 = 2/3

∴ The probability that the disc DOES NOT retain the same front and rear views after the flipping operation are 2/3.