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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 3.

Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 4.

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

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 May 10, 2019
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Let p be the probability of an even roll.

 

For option A

E[moves]=4p - 3(1-p) = 7p-3

 

For option B

E[moves]=5p-4(1-p) = 9p-4

 

Playing with the numbers it turns out that p=P[even roll]=3/4

I suggest you confirm this for yourself.

 

EA=21/4 - 12/4 = 9/4

EB = 27/4 - 16/4 = 11/4

 

EB offers the greater likelihood of moving closer to the finish line.

 May 11, 2019

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