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Simon wants to earn as many points as possible in one turn in a game. Two number cubes whose sides are numbered 1 through 6 are rolled. He is given two options for the manner in which points are awarded in the turn. OPTION A: If the sum of the rolls is a prime number, Simon receives 15 points. OPTION B: If the sum of the rolls is a multiple of 3, Simon receives 12 points. Which statement best explains the option he should choose? Simon should choose Option B. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options. Simon should choose Option A. The mathematical expectation of this option is 4 and is the greater mathematical expectation of the two options. Simon should choose Option B. The mathematical expectation of this option is 4 and is the greater mathematical expectati

 Mar 5, 2020
 #1
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Option A:  rolling a prime number:

     2  can be rolled only 1 way (1,1)

     3  can be rolled two ways (1,2) or (2,1)

     5  can be rolled four ways (1,4) or (2,3) or (3,2) or (4,1)

     7 can be rolled six ways (1,6) or (2,5) or (3,4) or (4,3) or (5,2) or (6,1)

   11 can be rolled two ways (5,6) or (6,5)

   There are 36 possible ways to roll two dice.

   The probability of rolling a prime number is:  (1 + 2 + 4 + 6 + 2) / 36  =  15/36

   Since rolling a prime number is worth 15 points, the expected value is  (15/36) x 15  =  6.25

 

Option B:  rolling a multiple of 3:

     3  can be rolled two ways (1,2) or (2,10

     6  can be rolled five ways (1,5) or (2,4) or (3,3) or (4,2) or (5,1)

     9  can be rolled four ways (3,6) or (4,5) or (5,4) or (6,3)

   12  can be rolled only 1 way (6,6)

   The probability of rolling a multiple of 3 is:  (3 + 6 + 9 + 12) / 36  =  12/36

   Since rolling a multiple of 3 is worth 12 points, the expected value is  (12/36) x 12  =  4

 

If you wish to maximize your expected point total choose Option A.

[I don't understand some of your expanation.]

 Mar 5, 2020

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