d20 Probability Question (come on you math geniuses!) [Archive] - Wizards Community

d20 Probability Question (come on you math geniuses!) [Archive] - Wizards Community

Post/Author/DateTime Post
Gadren
01-06-07, 06:12 PM If I roll a 20-sided die, there's a 5% chance of rolling 20, right?
So, what is the chance of rolling at least one 20 if I roll the die 5 times?
What is the chance of getting at least one 20 if I roll it 20 times?
Comus
01-06-07, 06:18 PM Dice don't have memory. The chance of rolling a 20 is 5% each time. Multiple attempts don't raise the percentage chance, merely the number of times that chance is checked.

Still, you've got about a 1 in 4 chance of getting a 20 within 5 rolls, and the chance approaches 1 in 1 for 20 rolls.
TheAngryFish
01-06-07, 06:29 PM it's a 5% chance, and therefore it is "probable" that one will roll one of every number 1-20 once, but, the odds of rolling the dice 20 times and landing on each of the numbers only once is not "likely".

If i were to roll a d20, and the result was a 13, i still have a 5% chance to roll it again, but because there is a 95% chance of rolling a different number, the odds of me getting two 13's in two rolls are not very high (1 in 400 I believe), though to get one 13 in one roll is always 5%
bitnine
01-06-07, 06:32 PM Still, you've got about a 1 in 4 chance of getting a 20 within 5 rolls, and the chance approaches 1 in 1 for 20 rolls.Erm, actually, the chance of getting a 20 in a set of n rolls uses 1-(1-p)^n, in this case 1-.95^n. That means you've got a 22.62% chance of seeing a 20 in 5 rolls, and a 64.15% chance of seeing a 20 in a set of 20 rolls.
Comus
01-06-07, 06:46 PM Erm, actually, the chance of getting a 20 in a set of n rolls uses 1-(1-p)^n, in this case 1-.95^n. That means you've got a 22.62% chance of seeing a 20 in 5 rolls, and a 64.15% chance of seeing a 20 in a set of 20 rolls.
And there you go - solid numbers from someone who actually took the appropriate maths. Primus knows geometry was always more my thing that probability.
Gadren
01-06-07, 09:18 PM Erm, actually, the chance of getting a 20 in a set of n rolls uses 1-(1-p)^n, in this case 1-.95^n. That means you've got a 22.62% chance of seeing a 20 in 5 rolls, and a 64.15% chance of seeing a 20 in a set of 20 rolls.

YAY! The answer I was looking for. Thankyou, Bitnine, for being good at math while the rest of us suck.
Kresalak
01-06-07, 09:40 PM Generally, an easy way to do this is to figure out your chance of failing to get that number, and raise that to the n power, where n is the number of dice you roll. So if you want to roll a 19 or 20, that's a 90% chance of not doing that. If you want to get a 19 or 20 within 4 rolls, you raise .9 to the 4th power, which is .94, or 0.6561, a 65.5% chance of failing. You have then, a 34.5% chance of succeeding.
Gadren
01-13-07, 12:09 AM Generally, an easy way to do this is to figure out your chance of failing to get that number, and raise that to the n power, where n is the number of dice you roll. So if you want to roll a 19 or 20, that's a 90% chance of not doing that. If you want to get a 19 or 20 within 4 rolls, you raise .9 to the 4th power, which is .94, or 0.6561, a 65.5% chance of failing. You have then, a 34.5% chance of succeeding.

Wow, that is much easier. Thankyou.

Post/Author/DateTime	Post
Gadren 01-06-07, 06:12 PM	If I roll a 20-sided die, there's a 5% chance of rolling 20, right? So, what is the chance of rolling at least one 20 if I roll the die 5 times? What is the chance of getting at least one 20 if I roll it 20 times?
Comus 01-06-07, 06:18 PM	Dice don't have memory. The chance of rolling a 20 is 5% each time. Multiple attempts don't raise the percentage chance, merely the number of times that chance is checked. Still, you've got about a 1 in 4 chance of getting a 20 within 5 rolls, and the chance approaches 1 in 1 for 20 rolls.
TheAngryFish 01-06-07, 06:29 PM	it's a 5% chance, and therefore it is "probable" that one will roll one of every number 1-20 once, but, the odds of rolling the dice 20 times and landing on each of the numbers only once is not "likely". If i were to roll a d20, and the result was a 13, i still have a 5% chance to roll it again, but because there is a 95% chance of rolling a different number, the odds of me getting two 13's in two rolls are not very high (1 in 400 I believe), though to get one 13 in one roll is always 5%
bitnine 01-06-07, 06:32 PM	Still, you've got about a 1 in 4 chance of getting a 20 within 5 rolls, and the chance approaches 1 in 1 for 20 rolls.Erm, actually, the chance of getting a 20 in a set of n rolls uses 1-(1-p)^n, in this case 1-.95^n. That means you've got a 22.62% chance of seeing a 20 in 5 rolls, and a 64.15% chance of seeing a 20 in a set of 20 rolls.
Comus 01-06-07, 06:46 PM	Erm, actually, the chance of getting a 20 in a set of n rolls uses 1-(1-p)^n, in this case 1-.95^n. That means you've got a 22.62% chance of seeing a 20 in 5 rolls, and a 64.15% chance of seeing a 20 in a set of 20 rolls. And there you go - solid numbers from someone who actually took the appropriate maths. Primus knows geometry was always more my thing that probability.
Gadren 01-06-07, 09:18 PM	Erm, actually, the chance of getting a 20 in a set of n rolls uses 1-(1-p)^n, in this case 1-.95^n. That means you've got a 22.62% chance of seeing a 20 in 5 rolls, and a 64.15% chance of seeing a 20 in a set of 20 rolls. YAY! The answer I was looking for. Thankyou, Bitnine, for being good at math while the rest of us suck.
Kresalak 01-06-07, 09:40 PM	Generally, an easy way to do this is to figure out your chance of failing to get that number, and raise that to the n power, where n is the number of dice you roll. So if you want to roll a 19 or 20, that's a 90% chance of not doing that. If you want to get a 19 or 20 within 4 rolls, you raise .9 to the 4th power, which is .94, or 0.6561, a 65.5% chance of failing. You have then, a 34.5% chance of succeeding.
Gadren 01-13-07, 12:09 AM	Generally, an easy way to do this is to figure out your chance of failing to get that number, and raise that to the n power, where n is the number of dice you roll. So if you want to roll a 19 or 20, that's a 90% chance of not doing that. If you want to get a 19 or 20 within 4 rolls, you raise .9 to the 4th power, which is .94, or 0.6561, a 65.5% chance of failing. You have then, a 34.5% chance of succeeding. Wow, that is much easier. Thankyou.