I have two four sided dice. Each die has 1, 2, 3, 4 as choices.
What the probability of the the second roll being greater than the first?
Examples:
1, 2
1, 4
3, 4
I used python to figure the probability of ~0.3750245 with 10 million trials, so close to 0.375 which is also 6/16 or 3/8
How can I get to 3/8 without programming it?
Best Answer
One simple way to think about problems like these is simply to count how many possible die rolls you have with two four sided die, and then count how many possible die rolls you can have where the second roll is greater than the first.
Then, $P(\text{second roll greater}) = \dfrac{\#\text{Rolls where the 2nd die is greater}}{\#\text{ Possible rolls}}$.
I claim that the possibilities for rolls where the second die is greater are: (1,2),(1,4),(1,3),(2,3),(2,4),(3,4).