Hannah and Corrine are playing a game by rolling two cubes, each numbered 1 through 6. If the sum of the numbers on the cubes is 7, Hannah wins. If the sum is not 7, Corrine wins. Corrine says Hannah can win only if the following occurs: 1 on the first cube, 6 on the second cube 2 on the first cube, 5 on the second cube 3 on the first cube, 4 on the second cube Which best explains if Corrine is correct?
Answer
A
Corrine is correct because there are no 7s on the cubes, so Hannah must roll a greater number on the second cube.
B
Corrine is not correct because Hannah can also roll doubles on the cubes, such as 3 on the first cube and 3 on the second cube or 4 on the first cube and 4 on the second cube.
C
Corrine is correct because there are only three ways to have a sum of 7 when the cubes are rolled.
D
Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.
Explanation
The two cubes are distinct, so the order of the numbers matters. Corrine listed three ways to make 7, but reversing each pair gives three more: (6, 1), (5, 2), and (4, 3). Those rolls also have a sum of 7, so Hannah can win in these additional ways. Choice D correctly explains that Corrine is not correct.
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