Question

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. find the probability the roll was a (a) sum of 12. the probability the roll was a sum of 12 is

Explanation:

Step1: Determine total number of outcomes

When rolling two dice, each die has 6 possible outcomes. By the fundamental counting principle, the total number of outcomes \(n(S)=6\times6 = 36\).

Step2: Determine number of favorable outcomes

The sum of two dice is 12. The only combination is \((6,6)\), so \(n(E)=1\).

Step3: Calculate probability

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting \(n(E) = 1\) and \(n(S)=36\), we get \(P(E)=\frac{1}{36}\).

Answer:

\(\frac{1}{36}\)