Answer:

Introduction:
In this question, we are asked to determine the property of an oily thin paper sheet. The options given are:
a) transparent
b) translucent
c) opaque
d) cannot be predicted

Explanation:
To determine the property of the oily thin paper sheet, we need to understand the terms transparent, translucent, and opaque.

Transparent:
- Transparent materials allow light to pass through them easily, without scattering the light.
- When an object is transparent, we are able to see objects clearly through it.
- Examples of transparent materials include glass, clear plastic, and air.

Translucent:
- Translucent materials allow some light to pass through them, but they also scatter the light.
- When an object is translucent, we can see shapes and shadows through it, but not clear details.
- Examples of translucent materials include frosted glass, wax paper, and some plastics.

Opaque:
- Opaque materials do not allow light to pass through them.
- When an object is opaque, we cannot see through it at all.
- Examples of opaque materials include wood, metal, and cardboard.

Analysis:
Based on the given options, we can eliminate options a) transparent and c) opaque because an oily thin paper sheet is not transparent like glass or plastic, nor is it opaque like wood or metal.

Conclusion:
Therefore, the correct answer is option b) translucent. An oily thin paper sheet allows some light to pass through it, but it also scatters the light, making it translucent.