Question

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

Answer 1

The sample space of throwing two dices is shown below:

(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)

We know that the probability of an event is given by:

`P=\frac{\text{ number of favorable results }}{\text{ number of possible results}}`

From the sample space above we notice that only three possible results will give either 2 or 11, then we have:

`P=(3)/(36)=0.083`

Multiplying by 100 to get the probability in percent form we have 8.3%

Therefore, the probability is 8.3%