when rolling two fair dice, the probability of rolling different sums is\nthe same.\ndifferent.
when rolling two fair dice, the probability of rolling different sums is\nthe same.\ndifferent.
Answer
Explanation:
Step1: Find 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 $6\times6 = 36$.
Step2: Find number of ways to get each sum
The minimum sum is $1 + 1=2$ and the maximum sum is $6+6 = 12$. For sum = 2: $(1,1)$ - 1 way. For sum = 3: $(1,2),(2,1)$ - 2 ways. For sum = 4: $(1,3),(2,2),(3,1)$ - 3 ways. For sum = 5: $(1,4),(2,3),(3,2),(4,1)$ - 4 ways. For sum = 6: $(1,5),(2,4),(3,3),(4,2),(5,1)$ - 5 ways. For sum = 7: $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$ - 6 ways. For sum = 8: $(2,6),(3,5),(4,4),(5,3),(6,2)$ - 5 ways. For sum = 9: $(3,6),(4,5),(5,4),(6,3)$ - 4 ways. For sum = 10: $(4,6),(5,5),(6,4)$ - 3 ways. For sum = 11: $(5,6),(6,5)$ - 2 ways. For sum = 12: $(6,6)$ - 1 way.
Step3: Analyze probabilities of different sums
Since the number of ways to get each sum is different, the probabilities of getting different sums (probability = number of favorable outcomes / total number of outcomes) are different.
Answer:
different.