Question

A cube is painted red on all its faces and then cut into 125 small cubes. One of the smaller cubes is then randomly selected. What is the probability that the cube selected will have at least 25 percent of its surface area painted red?

Answer 1

here for total 125 cubes

number of cubes with 3 sided painted =8 (since 1 small on each of 8 edges of bigger cube)

number of cubes with 2 sided painted =12*3 =36 (since 3 cubes on each of 12 line of big cube)

number of cubes with 1 sided painted =6*9 =54 (since 9 cubes on each of 6 of big cube)

since there are 6 sides of a cube, and a side with 2 or more painted side will have at least 25% of its side painted,

therefore  probability that the cube selected will have at least 25 percent of its surface area painted red

=(36+8)/125 =44/125