When 4 dice are thrown, it is observed that the sum appearing on them is 13, then the probability that 4 appears on at least one of the dice is

Numbers obtained on 4 dice where (sum = 13)
No of cases
(6,5,1,1), ---  12 ways

(6,4,2,1),-----24 ways

 (6,3,3,1)-----12 ways

, (6,3,2,2) ----12ways
(5, 5, 2,1 )     12
(5 ,4, 3,1)      24
(5,4, 2,2 )      12
(5,3,3,2 )       12
(4,4,4,1)         4
(4,4,3,2)       12
(4,3,3,3  )       4
Total 140 Cases
No.of favourable cases to get 4 on atleast one die =
24+24+12+4+12+4=80
Required probability  $=\frac{80}{140}=\frac{4}{7}$