When two different dice are thrown together, the sample space is given by
S=⎧⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪⎩(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)::::(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)⎫⎪
⎪
⎪
⎪⎬⎪
⎪
⎪
⎪⎭
∴n(S)=36
A≡ event that sum of nos is even.
A=⎧⎪⎨⎪⎩(1,1)(1,3)(1,5)(2,2)(2,4)(2,6)(3,1)(3,3)(3,5)(4,2)(4,4)(4,6)(5,1)(5,3)(5,5)(6,2)(6,4)(6,6)⎫⎪⎬⎪⎭
∴n(A)=18
P(A)=n(A)n(S)=1836=12
B= event that the product is even.
B≡⎧⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪⎩(1,2)(1,4)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,2)(3,4)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,2)(5,4)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)⎫⎪
⎪
⎪
⎪⎬⎪
⎪
⎪
⎪⎭
∴n(B)=27
P(B)=n(B)n(S)=2736=34