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Two different dice are thrown together. Find the probability that the numbers obtained have :
(i) even sum,
(ii) even product.
(i) even sum,
(ii) even product.
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(i) Number of outcomes with even sum =18
(1,1) (1,3) (1,5) (3,1) (3,3) (3,5) (5,1) (5,3) (5,5), (2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6)
P(even sum) = $\frac{18}{36}$ or $\frac{1}{2}$ (1
frac{1}{2} Mark)
(ii) Number of outcomes with even product = 27
(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)
P(even product) = $\frac{27}{36}$ or $\frac{3}{4}$ (1
frac{1}{2} Mark)
(1,1) (1,3) (1,5) (3,1) (3,3) (3,5) (5,1) (5,3) (5,5), (2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6)
P(even sum) = $\frac{18}{36}$ or $\frac{1}{2}$ (1
frac{1}{2} Mark)
(ii) Number of outcomes with even product = 27
(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)
P(even product) = $\frac{27}{36}$ or $\frac{3}{4}$ (1
frac{1}{2} Mark)