Question

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

Answer 1

http://openstudy.com/study#/updates/5580b809e4b0e4e582ab189b

Answer 2

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!