Two different dice are thrown together. Find the probability that the numbers obtained have

(i) even sum, and

(ii) even product.

(i) When two dies are thrown together, the possible outcomes are=

{(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)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)}

Total no of possible outcomes = 36

Outcomes having even sum=

{(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)}

Total No of favorable outcomes = 18

And we know,

Probability of an event

P(Getting even sum)

(ii)

When two dies are thrown together, the possible outcomes are=

{(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)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)}

Total no of possible outcomes = 36

Outcomes having even product=

{(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)}

Total No of favorable outcomes = 27

And we know,

Probability of an event

P(Getting even product)