Please someone help me to understand the first part of this question. In detailed explanation it is mentioned that for first row one payment is received. And for this payment it should go state 1 from 0 and then to state 3 from 1. Prob. Are given: 0.87 0.1 0 0.03 0 0.6 0.3 0.1 0. 0. 0.6. 0.4 0. 0. 0. 1 So for PV 30+0+0+0= 30 It goes from state 0 to state 1 and receive payment 30 and that have probability 0.1 But if life goes from state 1 to state 3 , so life doesn't get any benfit. And same goes for if life moves from state 0 to 3 and 2 to state 3 So in rest 3 cases life receive 0 benefit. Now second 30+30+0+0 If life moves from 0 to 1 , gets benefit 30 with 0.1 prob If life moves from state 2 to 1 gets = 30 with 0.6 prob If life moves from 0 to 3 = 0 Same for if life 2to 3=0 In 3rd row 30+30+30+0 If it moves 0to1 = 30 with prob 0.1 For 1to3 =30 with prob 0.6 For 2to 3 =30 with prob 0.6 For 0 to 3 =0 4th line doesn't come in this way I know this is little thing i might missing here or might be i missing entire concept of this question. Please review and help if possible