I agree with vp wiz on the human condition. The only hope I see for the 1 in 6 crowd is to give them more examples of why their math is incorrect.
With two dice let's compare the hard four (2-2) to the total of 3. Only one combination of 36 makes a hard four so the frequency is 36. With a total of 3 the frequency is 18. Thats because there are two combinations, 1-2 and 2-1, that make a total of 3. Unpaired dice come in 2 different orders. Die A can be the 1 and die B can be the 2. Or die A can be the 2 and die B the 1.
So a total of 3 is twice as likely to appear as the hard four. And in both combinations that make a 3 you can see that there is "at least one 2." The fact that unpaired dice come in 2 different orders is also true for 2-3, 2-4, 2-5, and 2-6....and that is why when "at least one of the dice is 2 it iis 10 to 1 against the other die being a 2.
Posted by: mickeycrimm@yahoo.com
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