if you roll two fair six - sided dice, what is the probability that the sum is 9 or higher?
if you roll two fair six - sided dice, what is the probability that the sum is 9 or higher?
Answer
Explanation:
Step1: Find total number of outcomes
When rolling two six - sided dice, each die has 6 possible outcomes. So the total number of outcomes when rolling two dice is $6\times6 = 36$ by the multiplication principle.
Step2: Find number of favorable outcomes
The possible pairs of dice values that give a sum of 9 or higher:
- Sum = 9: $(3,6),(4,5),(5,4),(6,3)$ (4 pairs)
- Sum = 10: $(4,6),(5,5),(6,4)$ (3 pairs)
- Sum = 11: $(5,6),(6,5)$ (2 pairs)
- Sum = 12: $(6,6)$ (1 pair) The total number of favorable outcomes is $4 + 3+2 + 1=10$.
Step3: Calculate the probability
The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P=\frac{10}{36}=\frac{5}{18}$.
Answer:
$\frac{5}{18}$