Question

Two dice are rolled. The first die shows "1," so its outcome is known. However, the other die rolls under the table where it cannot be seen. What is the probability that both of the dice show "1"?

Answer 1

`1/6`

Explanation:

We can roll two dice and get the following results:

`((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6),(1|,2,3,4,5,6,7),(2|,3,4,5,6,7,8),(3|,4,5,6,7,8,9),(4|,5,6,7,8,9,10),(5|,6,7,8,9,10,11),(6|,7,8,9,10,11,12))`

There are 36 possible rolls. However, we know the result of one of those rolls - it's a 1. On the chart, let's say the "row" 1 is known (I'll highlight it in red):

`((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6),(color(red)1|,2,3,4,5,6,7),(2|,3,4,5,6,7,8),(3|,4,5,6,7,8,9),(4|,5,6,7,8,9,10),(5|,6,7,8,9,10,11),(6|,7,8,9,10,11,12))`

So now there is a die whose result we don't know - it can be any one of six numbers. And so the probability of it being a 1 and therefore ending up with a roll of "snake eyes" is `1/6`