Explanation:

Sample space for a dice is

N(s) = (1,2,3,4,5,6)=6

total addition of occurring prime numbers while two dice are thrown

N(a) =(1,1),(1,2),(1,4),(1,6) , (2,1),(2,3),(2,5) , (3,2), (3,4), (4,1),(4,3), (5,2),(5,6), (6,1),(6,5)=15

as the question asking about getting prime numbers probability of throwing two dice so

N(s)* N(s)= 6*6

Final sample space will be

{(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)}=36

n(s)=36

So probability will be

P(e)=n(a)/ n(s)

P(e)= 15/36=5/12

Hence, option 1 is the correct answer.