Question

You are playing a game that uses two fair number cubes, If the total on the number cubes is either 2 or 5 onyour next turn, you win the game. What is the probability of winning on your next turn? Express your answer asa percent, If necessary, round your answer to the nearest tenthO 2.8%O 0.3%O 13.0%O 80.1%

Answer 1

Possible results: 36

$\begin{gathered} \lbrace(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3) \\ (3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\rbrace \end{gathered}$

Results that sum 2 or 5: 5

$\lbrace(1,1)(1,4)(2,3)(3,2)(4,1)\rbrace$

Then, the probability of winning on your next turn is:

$\begin{gathered} p(2or5)=\frac{\#\text{results that sum 2 or 5}}{\#possibl\text{e results}} \\ \\ p(2or5)=\frac{5}{36}=0.13 \\ \\ \\ \end{gathered}$In percentage: 13%