Question

when rolling two dice, the probability of rolling a sum of 8 or 9 is $\frac{1}{4}$. part 3 of 8 (c) sum greater than or equal to 8 when rolling two dice, the probability of rolling a sum greater than or equal to 8 is

Explanation:

Step1: Calculate total number of outcomes

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

Step2: Find number of favorable outcomes

The possible sums greater than or equal to 8:

• Sum = 8: \((2,6),(3,5),(4,4),(5,3),(6,2)\) → 5 outcomes
• Sum = 9: \((3,6),(4,5),(5,4),(6,3)\) → 4 outcomes
• Sum = 10: \((4,6),(5,5),(6,4)\) → 3 outcomes
• Sum = 11: \((5,6),(6,5)\) → 2 outcomes
• Sum = 12: \((6,6)\) → 1 outcome

Total favorable outcomes \(=5 + 4+3+2 + 1=15\)

Step3: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{15}{36}=\frac{5}{12}\)

Answer:

\(\frac{5}{12}\)