If a die is weighted, the first roll is no longer 1/6 probability to get a 7
Yes, actually, it is. No matter what the first die lands on, there is a 1 in 6 chance that the second die will land on the corresponding value necessary for a “7”. You could glue the first die to the table with “6” (or any other number) showing, and there will be a 1 in 6 chance that the second die will bring the sum to 7.
thebestaquaman@lemmy.world 17 hours ago
You need to roll two dice to get a sum of seven. Consider two fair dice: No matter what the first dice lands on, there’s a 1/6 probability that the second dice lands on the number you need to get a total of seven.
Consider now that one dice is weighted such that it always lands on 6. After you’ve thrown this dice, you throw the second dice, which has a 1/6 chance of landing on 1, so the probability of getting seven is still 1/6.
Of course, the order of the dice being thrown is irrelevant, and the same argument holds no matter how the first dice is weighted. Essentially, the probability of getting seven total is unaffected by the “first” dice, so it’s 1/6 no matter what.
meco03211@lemmy.world 17 hours ago
That’s if it’s perfectly weighted. If it’s weighted to roll a 6, it might not always land on 6. This would lower the chance of rolling a 7 depending on what the overall probability profile is on the weighted die.
KoboldCoterie@pawb.social 17 hours ago
No, it wouldn’t, as long as only one of the dice is weighted.
If it has a 95% chance to roll a 6, and a 5% chance to roll any other number, or a 100% chance to roll a 6, or a 0% chance to roll a 6, the chance is still 1 in 6 to roll a 7 with two dice (where either zero or one is weighted).
meco03211@lemmy.world 13 hours ago
Added an example
thebestaquaman@lemmy.world 16 hours ago
As mentioned by others: No matter how it’s weighed, and no matter what it lands on, there’s a 1/6 probability that the other dice will land on the number you need to get seven. The probability of getting seven is independent of the “first” dice.
meco03211@lemmy.world 13 hours ago
Added an example