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You are playing a game that uses two fair number cubes, If the total on the number cubes la either 11 or 2 onyour next turn, you win the game. What is the probability of winning on your next turn? Express your anawer ana percent, If necessary, round your answer to the nearest tenth,O 91.7%O 8.3%O 5.6%O 0.2%

Answer :

[tex]P=8.3\%[/tex]

1) Let's enlist the possible outcomes of two dices:

(1,1) (1,2), (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

There is a total of 36 outcomes

2) Let's bold the favorable outcome, either the sum of the cubes is 11 or 2:

(1,1) (1,2), (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

So there is a total of 3 favorable outcomes:

3) So let's write it as a Probability:

[tex]P=\frac{3}{36}=\frac{1}{12}=0.083[/tex]

This can also be written as a percentage multiplying by 100. Hence, the answer is 8.3%

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