Question

you are rolling two dice at the same time. what is the probability of rolling a sum of 5 or 9?

Explanation:

Step1: Determine total number of outcomes

When rolling two dice, each die has 6 outcomes. So total number of outcomes \(n(S)=6\times6 = 36\)

Step2: Find number of outcomes for sum of 5

The pairs \((x,y)\) such that \(x + y=5\) are \((1,4),(2,3),(3,2),(4,1)\). So \(n(5)=4\)

Step3: Find number of outcomes for sum of 9

The pairs \((x,y)\) such that \(x + y = 9\) are \((3,6),(4,5),(5,4),(6,3)\). So \(n(9)=4\)

Step4: Calculate probability

Let \(A\) be the event of getting sum of 5 or 9. Then \(n(A)=n(5)+n(9)=4 + 4=8\). Probability \(P(A)=\frac{n(A)}{n(S)}=\frac{8}{36}=\frac{2}{9}\)

Answer:

C. \(\frac{2}{9}\)