There are five solids called Platonic solids. Each Platonic solid has congruent faces, and congrunet angles, and they are shown below. Use the figures to compute the probabilities. Express your answers as fractions.

a. An octahedron has eight faces. If the octahedron faces are labeled with the numbers 1–8, and it is rolled, find the probability that it will land on a prime number.
b. The icosahedron has 20 congruent triangular faces. If they are labeled 1–20, and the icosahedron is rolled, what is the probability that it lands on a multiple of 3?

c. The dodecahedron has 12 congruent pentagonal faces. If they are labeled 1–12, and the dodecahedron is rolled, find the probability that it lands on a multiple of 3 and 2.
d. A tetrahedron has four congruent triangular faces labeled 10, 20, 30, and 40. Let T represent “the tetrahedron was rolled.” Let S represent the event “lands on a multiple of 7.” Find P(S|T).

Transcribed Image Text:

Tetrahedron Cube Octahedron Dodecahedron Icosahedron