If you roll a pair of fair dice, what is the probability of

  1. getting a sum of 1 ?
  2. getting a sum of 5 ?
  3. getting a sum of 12 ?

Answer : The sample space is

{(1,1), (1,2), (1,3),(1,4), (1,5), (1,6),

(2,1), (2,2), (2,3),(2,4), (2,5), (2,6),

(3,1), (3,2), (3,3),(3,4), (3,5), (3,6),

(4,1), (4,2), (4,3),(4,4), (4,5), (4,6),

(5,1), (5,2), (5,3),(5,4), (5,5), (5,6),

(6,1), (6,2), (6,3),(6,4), (6,5), (6,6)}

=> 36 Events

  1. Probability of getting a sum of 1 = 0/36 = 0
  2. Probability of getting a sum of 5 = P({(1,4),(2,3),(3,2),(4,1)}) = 4/36 = 0.1111
  3. Probability of getting a sum of 12 = P({(6,6)}) = 1/36 = 0.0278