Firstly, as a beginner I searched a lot of questions here and found out many useful information about probability of dice rolling. There are a lot of questions about 2 or 3 dice and many about 5 dice rolling but I didn't managed to get answers from there.
The problem involves rolling 5 dice (all are fair and 6 sided) at the same time.
What is probability of getting at least one number (for example number 3) in each 5 dice rolling?
This means that there are more combinations when this condition is fulfilled:
- one die with number 3, other four dice other numbers
- two dice with number 3, other three dice other numbers
- three dice with number 3, other two dice other numbers
- four dice with number 3, one die other numbers
- all five dice with number 3
I don't know when to use addition theorem of probability or multiplication theorem of probability.
I would like to know the method of calculation and the final result because I have already tried to calculate the probability but with no success (the professor only told me it's incorrect). I won't post it here because it's too long.
NOTE: This is not homework or task for school. In class we only worked simple scenario with 2 dice, I want to learn more about this and I went to consultations with professor and he didn't explained me the scenario with 5 dice)