Question

Two number cubes are rolled to determine how a token moves on a game board. The sides of

each number cube are numbered 1, 2, 3, 4, 5 and 6.
There are two options describing how the token will be moved.

Option A: If the product is even, move forward 4 spaces. Otherwise, move backward 8.

Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 9.

Use mathematical expectation to determine which option offers the greater likelihood of moving
closer to the finish line on the game board.

Which statement best explains the better option?


The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option A offers a greater likelihood of advancing to the finish line.

The mathematical expectation of Option A is . The mathematical expectation of Option B is 1. Option B offers a greater likelihood of advancing to the finish line.

The mathematical expectation of Option A is 1.5.The mathematical expectation of Option B is 1. Option A offers a greater likelihood of advancing to the finish line.

The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.

Answer 1

D. The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.

Explanation:

The result of a product is odd only when the two numbers are odds.

There are 6*6 = 36 possible outcomes when two dice are rolled. Only 9 of them are a combination of two odd numbers: {1, 1} {1, 3} {1, 5} {3, 1} {3, 3} {3, 5} {5, 1} {5, 3} {5, 5}. Then 36 - 9 = 27 outcomes are even.

P(even) = 27/36 = 0.75

Option A) Mathematical expectation: 0.75*4 + 0.25*(-8) = 1

Option B) Mathematical expectation: 0.75*5 + 0.25*(-9) = 1.5