SOLUTION: A man tossed two fair dice what is the conditional probability that the sum of the two dice will be 7, given that [5] (i) The sum is odd. (ii) The sum is greater than 6. (iii)

The sample space is the set of all pairs (a,b), where "a" and "b" are integer numbers from 1 to 6 inclusive,
representing possible outcomes tossing of two dice.


So, the sample space has 6*6 = 36 elements, and they all have the same probability of    each.


Now let's calculate the number of events with the odd sum of outcomes.


    2 elements have the sum 3 :  (1,2) and (2,1).

    4 elements have the sum 5 :  (1,4), (2,3), (3,2) and (4,1).

    6 elements have the sum 7 :  (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1)

    4 elements have the sum 9 :  (3,6), (4,5), (6,3) and (5,4)

    2 elements have the sum 11:  (5,6) and (6,5).


The total number of events with the odd sum is  2 + 4 + 6 + 4 + 2 = 18.


Of them, the number of events with the sum 7 is 6.


Therefore, the conditional probability under the problem's question is   =  =  = .    ANSWER