60-40 Split

Problem:

You have a fair $40$-sided and fair $60$-sided die in front of you. If you roll both, find the probability the $60$-sided die shows a strictly larger number than the $40$-sided die.

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This is a simple counting problem where we count the number of outcomes where the $60$-sided die shows a strictly larger number than the $40$-sided die and divide by the total number of outcomes.

We can do this by using the following code:

condition = []
all_possible = []

for i in range(1, 41):
    for j in range(1, 61):
        if i < j:
            condition.append((i, j))
        all_possible.append((i, j))

Which gives us:

$$\frac{1580}{2400} = \frac{79}{120} \approx 0.658$$