• # question_answer Two different dice are thrown together. Find the probability of: (i) getting a number greater than 3 on each die (ii) getting a total of 6 or 7 of the numbers on two dice

 Total outcomes = {(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)} $\Rightarrow$ Total no. of outcomes $=36$ (i) Let ${{E}_{1}}$ be the event of getting a number greater than 3 on each die. Favourable outcomes = {(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)} No. of favourable outcomes $=9$ $\therefore P({{E}_{1}})=\frac{9}{96}=\frac{1}{4}$ (ii) Let ${{E}_{2}}$ be the event of getting a total of 6 or 7 of the numbers on two dice. Favourable outcomes = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)} $\Rightarrow$ No. of favourable outcomes $=11$ $\therefore P({{E}_{2}})=\frac{11}{36}$