TS EAMCET · Maths · Probability

A cube having edge of length $5 cm$ is painted on all faces and then it is cut into equal cubes of unit volume. A small cube is selected at random and found that a face of it is painted, then the probability that two more faces of it are also painted is

A $\frac{27}{125}$
B $\frac{4}{49}$
C $\frac{1}{8}$
D $\frac{8}{125}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{4}{49}$

Step-by-step Solution

Detailed explanation

Let n smaller cubes of edge length 1 cm are obtained after cutting bigger cube of edge length 5 cm. Volume of bigger cube=n×Volume of smaller cube ⇒53=n×13 ⇒n=125 When the painted cube is cute into 125 small equal cubes, we have 3 faces painted…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A cube having edge of length 5 cm is painted on all faces and then it is cut into equal cubes of unit volume. A small cube is selected at random and found that a face of it is painted, then the probability that two more faces of it are also painted is

Step-by-step Solution

A cube having edge of length $5 cm$ is painted on all faces and then it is cut into equal cubes of unit volume. A small cube is selected at random and found that a face of it is painted, then the probability that two more faces of it are also painted is