Answer:
[tex]1/6[/tex]
Step-by-step explanation:
When we say, the difference of scores should be more than 3 it means that the difference can be 4 or 5.
Case 1: The difference of scores is 4.
The possible outcomes can be [tex](1,5), (5,1), (2,6) \text{ and }(6,2).[/tex] i.e. 4 number of cases are possible.
Case 2: The difference of scores is 5.
The possible outcomes can be [tex](1,6) \text{ and } (6,1)[/tex]. i.e. 2 number of cases.
Here, total number of favorable cases are 4 + 2 = 6.
Total number of cases, when two fair dice are rolled, are 36.
These cases are:
[tex][(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),\\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\..\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]}[/tex]
Formula:
[tex]\text{Probability of an event = } \frac{Number\ of\ favorable\ cases}{Total\ number\ of\ cases}[/tex]
Hence, the probability that the difference of scores is more than 3, at the roll of 2 dice, is [tex]\frac{6}{36}[/tex] i.e. [tex]\frac{1}{6}[/tex].
Hence, the required probability is [tex]\frac{1}{6}[/tex].
