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Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that :
(i) same number appears on both the dice ?
(ii) different number appears on both the dice ?
(i) same number appears on both the dice ?
(ii) different number appears on both the dice ?
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Possible outcomes are
$(1,1)(1,2), (1,3), (1,4), (1,5), (1,6)$
$(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)$
$(3,1)(3,2), (3,3), (3,4), (3,5), (3,6)$
$(4,1)(4,2), (4,3), (4,4), (4,5), (4,6)$
$(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)$
$(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)$ (1 Mark)
(i) $P(\text{same number appears on both the dice}) = \frac{6}{36}$ or $\frac{1}{6}$ (1 Mark)
(ii) $P(\text{different numbers appear on both the dice}) = 1 - \frac{1}{6} = \frac{5}{6}$ (1 Mark)
$(1,1)(1,2), (1,3), (1,4), (1,5), (1,6)$
$(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)$
$(3,1)(3,2), (3,3), (3,4), (3,5), (3,6)$
$(4,1)(4,2), (4,3), (4,4), (4,5), (4,6)$
$(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)$
$(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)$ (1 Mark)
(i) $P(\text{same number appears on both the dice}) = \frac{6}{36}$ or $\frac{1}{6}$ (1 Mark)
(ii) $P(\text{different numbers appear on both the dice}) = 1 - \frac{1}{6} = \frac{5}{6}$ (1 Mark)