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

(i) even sum, and

(ii) even product.[CBSE 2017]

(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)