We obtain following prime sum in three throws of dice; 3,5,7,11,13 and 17 And sum in from of 4m+1 are, 5,13 and 17 Following are favourable outcomes for above sums (1,2,2),(2,1,2),(2,2,1) (3,1,1),(1,3,1),(1,1,3) (5,3,3),(3,5,3),(3,3,5) (6,6,1),(1,6,6),(6,1,6) (4,4,5),(5,4,4),(4,5,4) (2,6,5),(6,2,5),(5,2,6) ......... etc. Total number of out comes of obtaining sum a prime of from 4m+1′=sum5(6 times )+sum13(21 times )+ sum 17(3 times )=30 cares. Total number of possible outcomes =6×6×6=216 cares Hence, required probability =‌