Question

what is the probability that you roll two dice and get a 5 and 3? answer as a fraction.

Explanation:

Step1: Calculate the total number of outcomes

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

Step2: Calculate the number of favorable outcomes

The favorable outcomes for getting a 5 and a 3 are two cases: \((5,3)\) and \((3,5)\). So \(n(A)=2\)

Step3: Calculate the probability

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\). Substituting the values, we get \(P(A)=\frac{2}{36}=\frac{1}{18}\)

Answer:

\(\frac{1}{18}\)