Your average science guy, Linux nerd, and Minecraft player. Left Reddit for this place and haven’t looked back. :)

Website: lostxor.com

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Cake day: March 3rd, 2024

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  • You’re right! Let’s say we have two dice:

    D₁ is fair and has a 1/6 probability of rolling each number from 1-6.
    D₂ is weighted, with probabilities P₁, P₂, P₃, P₄, P₅, P₆ to roll each number.

    We roll D₁, and get a number with the following probability distribution:
    1: 1/6
    2: 1/6
    3: 1/6
    4: 1/6
    5: 1/6
    6: 1/6

    We roll D₂, and get a number with the following probability distribution:
    1: P₁
    2: P₂
    3: P₃
    4: P₄
    5: P₅
    6: P₆

    We find the probabilities of every combination of rolls that yields a 7:
    1+6: 1/6 P₁
    2+5: 1/6 P₂
    3+4: 1/6 P₃
    4+3: 1/6 P₄
    5+2: 1/6 P₅
    6+1: 1/6 P₆

    Adding these together to get the total probability of rolling a 7, we get 1/6 (P₁ + P₂ + P₃ + P₄ + P₅ + P₆). Since the probabilities of rolling each number must sum to 1, we get a probability of 1/6 to roll a 7, and your gut is right. :)

    7 is the only number where this property holds. Other numbers will have a probability dependent on the weighting of the die, which could be calculated with a similar method.