A question about dice probability calculation

[TheNaturalStep]

A question about probability calculation
What is the probability that the sum from two dices are under 9, i don’t know a fast way to calculate that :(, instead i calculated it manually by listing all possible event.
Divided by the total number of outcomes 6*6=36

And something else that I can not understand,
p=probability that this happen

Case 1
dice (1,1), dice (1,1), <-> is one event <-> 2p
case 2
dice(1,2) and dice(2,1) <-> is two events <->2p

How come case one gets 1 event and 2p when case 2 gets two events and 2p ...

Kindly TNS ...

 

[rock.freak667]

If you get more than 9(assuming that you meant sum>9 and not equal to 9) you can get (6,3) or (6,4) or (6,5) or (6,6) or (5,5) or (5,4) <---- these gives you the possibilities to get a sum$\geq$9. NOTE: this follows the order, (dice1,dice2)

so to get (6,3)=$\frac{1}{6}*\frac{1}{3}*2!=\frac{1}{9}$

since all the possibilities will be similar to that it will simply be $\frac{1}{9}*6$ which is $\frac{2}{3}$ but this is to find P(sum$\geq$9) so then to find what you want is simply 1-P(sum$\geq$9)

 

[HallsofIvy]

And something else that I can not understand,
p=probability that this happen

Case 1
dice (1,1), dice (1,1), <-> is one event <-> 2p
case 2
dice(1,2) and dice(2,1) <-> is two events <->2p

How come case one gets 1 event and 2p when case 2 gets two events and 2p ...

Kindly TNS ...

If you were calculating the probability of getting a 2 on a pair of dice, there is only one way that can happen. Die "A" is a 1 and die "B" is a 1. Probability of rolling a 2 is 1/36.
If you were calculating the probability of getting a 3 on a pair of dice, there are two ways that can happen. Die "A" is a 2 and die "B" is a 1 or die "A" is a 1 and die "B" is a 2. Probability of rolling a 3 is 2/36= 1/18.

 

[TheNaturalStep]

Thank you very much for your replies, i think it is clear now.

Kindly TNS