@makkahn28 - Good to know you are following us on twitter as well
Happy long weekend to you and to our fellow Community members!
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?
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.
And we already know that at least one shows a two, so chances other dice to roll 2 is 1/6 = 16.67%.
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.