Say, I have a die. When we roll a die we know that one side will face up and four sides will face north, west, east and south (assuming the die is always in the right position).
We also know that the sum of the sides is always 7. For example if one side is 6 then the opposite side will be 1. That means the probability of sum of east + west or north + south is 7 is always 1.
My questions are:
- How to compute the probability of getting 4 on the north given that six is on top?
- What if there are two dice, what is the probability of getting 3 facing West in one die and getting 4 facing East in the other die given one of the die has 6 facing the top?
So far, my approach is:
The sample size is, the possible number on the top x the remaining possible number facing a direction x the matched number x the remaining possible number x the matched number.
There are 6 possible numbers on top, so 6. There are 5 possible number facing North, so 5. There are only one possible number for South, so 1. There are 3 possible number facing West, so 4. There are one possible number facing East, so 1.
S = 6 x 5 x 1 x 3 x 1 x 24 (because there are 24 combinations of North, South, West and East).
Am I in the right direction?