Question

Answer the following questions about conditional probability and Bayes theorem a. You roll 2 dice and record the sum i. Write the sample space ii. What is the probability of the sum being 10? ii. What is the probability that at least one of the die values was a 6 given that the sum was greater than or equal to 7?

Answer 1

a) The faces values of each die are as 1, 2, 3, 4, 5 , and 6.

i) The sum of the two dies are from 2 to 12

So sample space is { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }.

ii) Here we want to find probability of the sum being 10

Total ways = 6*6 = 36

possible ways = 3

as { 4,6}; {6, 4}; and {5, 5}

so required probability = 3/36 = 1/9 = 01111

iii) It is given that the sum was greater than or equal to 7

So the total ways of the above events = 6 + 5 + 4 + 3 +2 + 1 = 21

Possible ways =11 as {1, 6}; {6, 1}; {2, 6}; {6, 2}; {3, 6}; {6, 3}; {4,6}; {6,4} ; {5,6}; {6,5}; {6,6}.

So required probability = 11/21 = 052381