Dice probability.

Question

You want to find the probability of rolling a sum of 9 on two dice and then rolling a sum of 10 on the next roll. Tell whether these events are independent or dependent.

Answer 1

 

There are 36 possible outcomes with two dice.

 

(die1, die2)

 

 9 can be rolled 4 ways: (4,5),(5,4),(6,3), or (3,6) 

10 can be rolled 3 ways: (4,6),(6,4), or (5,5)

 

Thus:  Pr{9 rolled} = 4/36 = 1/9

          Pr{10 rolled} = 3/36 = 1/12

 

The two rolls are independent, the outcome of a 9 has no bearing on the value of the next roll (fair dice assumed).

 

Therefore, Pr{10 rolled | 9 just rolled} = Pr(9}*Pr{10} = (1/9)(1/12) = 1/108.