Question

Two dice are rolled, find the probability that the sum is i) equal to 1 ii) equal to 4 iii) less than 13

Answer 1

The sample space S of two dice is shown below.

 

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) }

 

Let E be the event "sum equal to 1". There are no outcomes which correspond to a sum equal to 1, hence  
P(E) = n(E) / n(S) = 0 / 36 = 0

 

(b) Three possible ouctcomes give a sum equal to 4: E = {(1,3),(2,2),(3,1)}, hence.  
P(E) = n(E) / n(S) = 3 / 36 = 1 / 12

 

(c) All possible ouctcomes, E = S, give a sum less than 13, hence.  
b P(E) = n(E) / n(S) = 36 / 36 = 1

hope this helps you out. .....