Question

In a single throw of two dice, find (i) P (an odd number on the first die and a 6 on the second) (ii) P (a number greater than 3 on each die) (iii) P (a total of 10) (iv) P (a total greater than 8) (v) P (a total of 9 or 11) Select the correct answer from above options

Answer 1

Probability of occurrence of an event = (Total number of favorable outcomes) / (Total number of outcomes) Possible outcomes are as follow: (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 number of outcomes = 36 (i) Pick favorable entries: (1, 6), (3, 6), (5, 6) Total number of favorable outcomes = 3 P (an odd number on the first die and a 6 on the second) = 3/36 = 1/12 (ii) Pick favorable entries: (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) Total number of favorable outcomes = 9 P (a number greater than 3 on each die) = 9/36 = 1/4 (iii) Pick favorable entries: (4, 6), (5, 5), (6, 4) Total number of favorable outcomes = 3 P (a total of 10) = 3/36 = 1/12 (iv) Pick favorable entries: (3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6) Total number of favorable outcomes = 10 P (a total greater than 8) = 10/36 = 5/18 (v) Pick favorable entries: (3, 6), (4, 5), (5, 4), (6, 3), (6, 5) , (5, 6) Total number of favorable outcomes = 6 P (a total of 9 or 11) = 6/36 = 1/6