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MTH219 Fundamentals of Statistics and Probability, SUSS, Singapore: A dodecahedron is a regular polyhedron with 12 pentagonal faces. It is one of the 5 possible 3-dimensional shapes
 University SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) Subject Statistics and Probability
Posted on: 4th Oct 2023

# MTH219 Fundamentals of Statistics and Probability, SUSS, Singapore: A dodecahedron is a regular polyhedron with 12 pentagonal faces. It is one of the 5 possible 3-dimensional shapes

Question

A dodecahedron is a regular polyhedron with 12 pentagonal faces. It is one of the 5 possible 3-dimensional shapes where every face is the same and every corner looks the same, known as a Platonic solid. The other Platonic Solids are 4-sided (tetrahedron), 6-sided (cube), 8-sided (octahedron), and 20-sided (icosahedron).

A dice was made from a dodecahedron, and the faces were numbered 1 to 12. This dice was rolled once. We call the number from a 12-sided dice a “d12”.

(a) Calculate the mean and variance of the d12.

(b) A game involves a board with a series of numbered squares (Numbers 1 to 200), and players take turns rolling a 12-sided die and moving their game piece forward along the squares based on the number rolled. For example, if a player rolls a 4, they move their piece forward 4 squares. In other words, this is a snake and ladder game without any complicated rules such as the snakes and ladders.

Calculate the average number of d12 rolls needed to reach the 200th square.

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