Respuesta :
The probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces will be 0.0714.
We have,
Total number of smaller cubes = 64
Side of larger cube = 4 units,
And,
Two faces of the larger cube that share an edge are painted blue,
And the cube is disassembled into 64 unit cubes.
Now,
If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.
And,
Also, from the 28 cubes painted only 4 have exactly two painted faces.
So,
Using combination formula,
[tex]^n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
Now,
Ways to select 2 cubes from the 64 = ⁶⁴C₂ ,
And,
Ways to select one cube with exactly two painted faces and one cube with no painted faces = ⁴C₁ × ³⁶C₁
So,
The probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces,
i.e.
Probability = [tex]\frac{ ^{4}C_{1}* ^{36}C_{1}}{ ^{64}C_{2}}[/tex]
On solving we get,
Probability = 0.0714
So,
The Probability of two selected unit cubes is 0.0174.
Hence we can say that the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces will be 0.0714.
Learn more about probability here
https://brainly.com/question/11234923
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