4. An octahedron is a solid with eight faces. Each face is shaped like a triangl

Question

4. An octahedron is a solid with eight faces. Each face is shaped like a triangle with four faces a "1" is painted. On three faces a "3" is painted. And, on one face a "5" is painted. The experiment consists of tossing the solid twice, and X is the sum of the numbers on the top face each time. a. List the possible values of X. (Use a table to show the sample space.) b. Compute the probability distribution for X to four decimal places. c. State the meaning of P(4) LS d. 44.5 d. Approximate ,to one decimal place.

Explanation / Answer

a) Possible values of X = 2, 4 , 6 , 8 , 10

b) P(X = 2) = 0.25

P(X = 4) = 4/8 * 3/8 * 2 = 0.375

P(X = 6) = 4/8 * 1/8 * 2 + 3/8 * 3/8 = 0.2656

P(X = 8) = 3/8 * 1/8 * 2 = 0.0938

P(X = 10) = 1/8 * 1/8 = 0.0156

c) P(4) = P(X = 4) = 0.375

d) , E(X) = 2 * 0.25 + 4 * 0.375 + 6 * 0.2656 + 8 * 0.0938 + 10 * 0.0156 = 4.5

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