Problem
During a charity Las Vegas Casino Night, Rosie plays craps and gets to roll the dice. Use the sample space for rolling two dice as shown below. Express your answers as reduced fractions. Second die \begin{tabular}{l|lllllll} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\ 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6 \\ 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\ 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6 \\ First die & 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\ \hline 5 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6 \end{tabular} (a) Sum of 12 The probability that Rosie rolled a sum of 12 is (b)Sum that is even. The probability that Rosie rolled a sum that is even is
Solution
Step 1 ：The question asks for the probability of rolling a sum of 12 when two dice are rolled.
Step 2 ：There are 36 possible outcomes when rolling two dice (6 outcomes for the first die times 6 outcomes for the second die).
Step 3 ：Looking at the table, it's clear that the only way to get a sum of 12 is by rolling a 6 on both dice.
Step 4 ：So, the probability of rolling a sum of 12 is the number of outcomes that sum to 12 divided by the total number of outcomes.
Step 5 ：Final Answer: The probability that Rosie rolled a sum of 12 is \(\boxed{\frac{1}{36}}\).
