Question

7. Two fair six sided dice are rolled.

(i) What is the probability that the sum of the two results is 6?
(ii) What is the probability that the larger value of the two results is 4?

(iii) What is the probability that the both results are at most 4?
(iv) What is the probability that the number 3 appears at least once?

Answer 1

7) total sample sapce = 6 * 6 = 36

i) Sample outcome for sum of 6 = {(1,5), (2,4), (3,3), (4,2), (5,1)}

P(sum of 6) = 5/36

ii) Sample outcome for larger value of the two results is 4 = {(1,4), (2,4), (3,4), (4,4), (4,3), (4,2), (4,1)}

P(larger value of the two results is 4) = 7/36

iii) sample outcome for both results are at most 4 = {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}

P(both results are at most 4) = 16/36 = 4/9

iv) P(number 3 appears at least once) = 1 - P(number 3 does not appear)

                                                              = 1 - (5/6 * 5/6)

                                                              = 1 - 25/36

                                                              = 11/36