Rolling a red and a green die determine Psum is 4Leave answe

Rolling a red and a green die, determine P(sum is 4).(Leave answer as a fraction.

Solution

a red die and a green die are rolled.

for the red die any one number from (1,2,3,4,5,6) occurs with probability 1/6

for the green die also any one number from (1,2,3,4,5,6) occurs with probability 1/6

so the sample space is

S={(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)}

where the first number denotes the occurance of the red die and second number denotes the occurance of the green die.

any one of the elements of S will occur with probability 1/6² when the two dice will be rolled.

so P[sum is 4]=P[(1,3),(3,1),(2,2)]=P[(1,3)]+P[(3,1)]+P(2,2)] [as these events are mutually disjoint]

                     =1/6²+1/6²+1/6²=3/36=1/12 [answer]