Q1 · hard · AI-verified
Two standard dice are rolled together. Given that at least one die shows a 6, what is the probability that the sum is greater than 8?
- 6/11
- 7/11
- 8/11
- 9/11
Q2 · hard · AI-verified
A cube is painted with 6 different colors (one color per face) and then cut into 27 smaller identical cubes. How many of the smaller cubes will have exactly 3 different colors?
- 0
- 6
- 8
- 12
Q3 · hard · AI-verified
A dice is constructed such that the sum of numbers on opposite faces is always 7. If the dice is rolled and lands showing 3 on top, 2 on the front face, and 5 on the right face, what number is on the back face?
- 1
- 4
- 5
- 6
Q4 · hard · AI-verified
A cube has vertices labeled A through H. If face ABCD is painted red and face EFGH is painted blue, and the cube is then cut into 8 smaller cubes, how many smaller cubes will have both red and blue paint?
- 0
- 2
- 4
- 8
Q5 · hard · AI-verified
A large cube is made up of 216 unit cubes. If this large cube is painted blue on all external faces and then disassembled, how many unit cubes will have blue paint on exactly three faces?
- 8
- 12
- 24
- 36