Quote:
Originally Posted by Puzzled
Hi
No not remotely getting hung up on double 6 and as stated in the OP I don't think dice combos apply here because we're looking for a single number so there is no connection between the dice or their rolls.
In your first post there you say:
"Therefore, you need to roll the second die. You roll the second die and get a six. This happens 5 of 36 times "
This can not possibly be true. The chances of the 2nd die rolling a 6 is and always will be 1 in 6, just as it is for any die. What happened before you roll it is of no consequence. The odds of rolling a 6 are 1 in 6
If you didn't understand that, let me try to explain this more simply for you then. Let's look at the manual way first:
Manual Way
First, look up above. Count the number of possible dice rolls. It's 36, right?
Second, look up above. Count the number of possible dice rolls that have one or more sixes in them? It's 11, right?
Third, do we agree that every combination has the same probability of being rolled? I'm going to guess you agree.
Therefore, it's obviously 11 out of 36. That's the "hard" way. Manually count all possibilities and manually count all that contain the attribute for which we are looking.
Mathematical Way
Now, let me take a shot at showing you why you are making a mathematical mistake, again.
Define your goal: To roll a 6.
Define your parameters: You have two dice. A roll of a 6 on either die meets the goal. It doesn't matter if you roll one 6 or two 6s.
I think we all agree so far.
Just for ease, let's say you roll the dice one at a time. We agree that on the first die, there are six possibilities and one of those possibilities is rolling a 6. So, the odds of the first die containing a six is one out of six. We agree on that, right?
So, to say it another way, six out of 36 times, we do not care what is on the second die. We've met our goal. 30 out of 36 times, we care what is on the second die. Still with me?
Now, for the 30 times that we care about the second die, we agree that there is a one out of six chance that it will be a 6 for the times we care what it is, right? Here is where you get hung up, though. You just say there is a one out of six chance of rolling a 6 and leaving it hang there. That's incomplete because there is a seventh variable for the second die and that is, we don't care what is on it. So, the odds of rolling a 6 with the second die is 5 out of 36, not 6 out of 36. To spell it out:
- 5x - Roll a 1
- 5x - Roll a 2
- 5x - Roll a 3
- 5x - Roll a 4
- 5x - Roll a 5
- 5x - Roll a 6
- 6x - We Don't Care
Therefore, it's not 6/36 + 6/36 = 12/36 (or 1/3). It is 6/36 + 5/36 = 11/36.
Just to prove this, let's say you have six dice and roll them all needing just one 6. By your math, 1/6 + 1/6 + 1/6 +1/6 + 1/6 +1/6 = 6/6 or 1. By your math, it's impossible to roll six dice and not roll a 6. We know that is not true, though. The true answer would be 6/36 + 5/36 + 4/36 + 3/36 + 2/36 + 1/36 or 21/36.
Also the post directly above this one is absolutely correct, but I thought this might be easier for you to understand.
Last edited by Gobbs23; 09-10-2020 at 04:09 PM.
Reason: Added last paragraph