An experiment consists of rolling a pair of regular (i.c., sixfaced and balanced} dice repeatedly and tracking the sum of the numbers obtained on each roll. Let B denote the event ofobtaining a sum of3 before obtaining a sum of 7. We want to find 13(3). b} The sequence of events { Hi } is pairwise disjoint Consider two events Hi and Hi i H The event Hi will be a set of sequence of die rolls which will have numbers otherthan 3 or 7 from 1 to i-1 rolls and have 3 on the i\" roll. The event Hi will be a set of sequence of die rolls which will have numbers other than 3 or 7 from 1 to H rolls and have 3 on the j'h roll. If SC HI Then during the Fh roll, we will obtain 3 if i j. The sequence it won't belong to any of the possibilities in Hj, as we will have only values equal to 3 or 7 in x on the jth roll. 50 the values will differ at the jth position. Thus the sequence of events {H} is pairwise disjoint Step 3: c) B is the event of obtaining the sum of 3 before 7. Hi is the event of obtaining the sum of 3 before 7 exactly on the ith roll. Event B can also be written as the event of obtaining the sum of 3 before 7 on either the first or second or third or .. Since Hi are pairwise disjoint for different values of i. B will be the union of the events for different values of i. This will go on from the first roll to the infinite possibility of rolls. B = Uj HI Thus we have obtained an explicit expression for B in terms of obtainable events Hi.