## anonymous one year ago Kimiko and miko are playing a game in which each girl rolls a number cube. If the sum of the numbers is a prime number, then miko. Otherwise Kimiko wins. Find the sample space. how do you do this idk how to do this

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1. kropot72
2. ybarrap

The sum of two dice: 1 2 3 4 5 6 +------------------- 1 | $$\color{red}2$$ $$\color{red}3$$ 4 $$\color{red}5$$ 6 $$\color{red}7$$ 2 | $$\color{red}3$$ 4 $$\color{red}5$$ 6 $$\color{red}7$$ 8 3 | 4 $$\color{red}7$$ 6 $$\color{red}7$$ 8 9 4 | $$\color{red}5$$ 6 $$\color{red}7$$ 8 9 10 5 | 6 $$\color{red}7$$ 8 9 10 $$\color{red}{11}$$ 6 | $$\color{red}7$$ 8 9 10 $$\color{red}{11}$$ 12 Count all $$\color{red}{\bf{Reds}}$$, those are the prime numbers, $$p$$ Count all the possibilities, 36 $$P(Miko~wins)=\cfrac{p}{36}\\ P(Kimiko~wins)=1-\cfrac{p}{36}\\$$ Miko wins if $$P(Miko~wins)>P(Kimiko~wins)$$ That's it!