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Retraité / Retired

Wishing you a fun-filled long weekend

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Mayor / Maire

Re: Wishing you a fun-filled long weekend

Thanks. I received a PM Tweet too. Thanks

Retraité / Retired

Re: Wishing you a fun-filled long weekend

@makkahn28 - Good to know you are following us on twitter as well Cat Happy

Happy long weekend to you and to our fellow Community members! 

Good Citizen / Bon Citoyen

Re: Wishing you a fun-filled long weekend

Yes, thanks.

 

Something for the geniuses among us to ponder on the way to the cottage...

 

If you roll two dice, and at least one shows a 2, then what is the chance that also the other die shows a 2?

Retraité / Retired

Re: Wishing you a fun-filled long weekend

Now let's see.. we have 2 dice. If you roll one die, it can land in 6 different ways. If you roll two, they can land in 36 different ways, i.e., 6 X 6. Cat Frustrated

 

And we already know that at least one shows a two, so chances other dice to roll 2 is 1/6 = 16.67%.

Mayor / Maire

Re: Wishing you a fun-filled long weekend

Take care of you on this long weekend !

Legend

Re: Wishing you a fun-filled long weekend

I'll be resting my sore back in bed. Blah!
Good Citizen / Bon Citoyen

Re: Wishing you a fun-filled long weekend

Of the 36 possible theoretical rolls of two dice: 25 rolls show no 2 on each: 10 rolls show only one 2 on each; and 1 roll shows two 2's.

When at least one die shows 2, for every 10 rolls of only one 2 each there will be 1 roll of both dice showing a 2.  That means one in eleven times overall there will be a double 2. (Note that the required single 2 may be on either die.  If the 2 is on the die on the left, then there are five non-2 possibilities for the die on the right; and if the 2 is on the die on the right, then there are five non-2 possibilities for the die on the left.)

However, we don't have to think like mathematicians.  I maintain that a better answer is one in six times.  The condition that "at least one die is a 2" is the same as "one or more of the dice is a 2".  Hence, the only way to properly and fully meet that condition in terms of two dice by consecutive rolls would be to look at only one die first.  Were it a 2, then would have the "one a 2", and possibly the "or more a 2" by the other die.  But, were it not a 2, then not possibly the "or more a 2" by the two dice in the roll.  Two dice must be considered separately, ie, not as one possible outcome together of a (simultaneous) set of such possible outcomes.

Note that in the sentence, "Of the 36 possible theoretical rolls of two dice: 25 rolls show no 2 on each: 10 rolls show exactly one 2 on each; and 1 roll has both dice showing a 2 at the same time," the operative word is "and".  Writing "or" instead of "and" would be the mathematical approach to the condition "at least one die is a 2"; but not the physical, real-life approach to this exercise in general.
Model Citizen / Citoyen Modèle

Re: Wishing you a fun-filled long weekend

Hope everyone is having a great and safe long weekend. Smiley Happy