Question

In Bob Guest's office there are two glass jars filled with dice in the shapes of the five Platonic solids. There are Tetrahedrons (4 sided), Cubes (6 sided) also known as Hexahedrons, Octahedrons (8 sided), Dodecahedrons (12 sided) and Icosahedrons (20 sided). The dice also come in a variety of solid and translucent colors. The table below details the number of dice of each shape and color combination in the jars Tetrahedron Cube Octahedron Dodecahedron cosahedron Total solid translucent Total 15 10 25 13 15 28 63 63 126 12 10 24 23 26 (Round all answers to 5 decimal places) A. Two dice are randomly selected with replacement, what is the probability that they are both Octahedrons? B. Two dice are randomly selected without replacement, what is the probability that they are both Octahedrons?

Answer 1

A) In case of with replacement:

P(Both Octahedrons) = (28/126)*(28/126) = 0.04938

B) In case of without replacement:

P(Both Octahedrons) = (28/126)*(27/125) = 0.048