Math problem - Dice outcomes

[Zook]

math and other thinking skills are not taught well.

when faced with a problem one way to help is to reduce it so it is easier to think about.

take this and change it to two coins...

if that doesn't help that's ok but please realize you should not have strong opinions on anything.

zook

 

[Protoss]

Yeah, you haven't summed the probabilities to 1 in the second brackets:
"(4 OR 6 on die #1) AND (( the other on #2 ) OR (the other on #3))

( 1/6+1/6 ) x ((1/6) + (1/6))"
That should read: (1/6 + 1/6) x ((1/6)(6/6) + (5/6)(1/6)) - this shows the odds of rolling one of the numbers on the first die, then the other on at least one of the two next rolls. This is 22/216, and accounts for rolling 4 or 6 three times. Your mistake boils down to the problem that others have had in this thread - the odds of rolling the second number on the third throw but NOT the second is where that 5/6 comes in.

Yes of course there is a big difference between rolling only one 4 and only one 6 in three rolls versus "at least" one 4 or at least one 6 in three rolls ( where say a 4 and a 4 and a 6 would be acceptable )

Perry: "calcified" haha that's funny I resisted for a while but ultimately couldn't help myself. It's good for you !!

 

[Anynym]

It is permutations and combinations question... and I was just too lazy, have no incentive, to do the mathematics.

Perry

Yup.

The particular field of mathematics is also referred to as "Combinatorics", and is usually paired with a related field referred to as "Optimization".

 

[benstt]

Everyone has their geek hat on. This is basic probability, analyzed with elements of combinatorics in the case of dice. Ie countable outcomes.

Point is to distinguish it from statistics, which is more to do with the presentation and analysis of data. Ie tabulating outcomes, predicting them, etc. Statistical studies use probability theory to assess hypotheses about data, establish predictions, etc.

For example, the number of times you get a '1' in 100 die rolls is a statistic. Analyzing whether that outcome comes from a fair die involves uses probability theory. As would establishing a prediction interval for that statistic.

The neuron pathways are alive on this one.

 

[shack]

Now if it were a pretty lady asking and there are prospects of a certain kind of reward, I would be happy to punch the figures into a calculator and work them out.

Sounds like a "conditioned response" to me.