Two dice are thrown independently. Let A be the event that the number appeared on the 1 st die is less than the number appeared on the 2 nd die, B be the event that the number appeared on the 1 st die is even and that on the second die is odd, and C be the event that the number appeared on the 1 st die is odd and that on the 2 nd is even. Then

Step-by-step solution

Given, A : No. on 1 st  die < No. on 2 nd  die A = ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 4 ) , ( 1 , 5 ) , ( 1 , 6 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 2 , 6 ) , ( 3 , 4 ) , ( 3 , 5 ) , ( 3 , 6 ) , ( 4 , 5 ) , ( 4 , 6 ) , ( 5 , 6 ) ∴   n ( A ) = 15 B : No. on 1 st  die = even & No. of 2 nd  die = odd B = ( 2 , 1 ) , ( 2 , 3 ) , ( 2 , 5 ) , ( 4 , 1 ) , ( 4 , 3 ) , ( 4 , 5 ) ,   ( 6 , 1 ) , ( 6 , 3 ) , ( 6 , 5 ) ∴   n ( B ) = 9 C : No. on 1 st  die = odd &