Question
A die is thrown and the sum of the numbers appearing is observed to be 7. What is the conditional probability that the number 2 has appeared at least once.
Solution
Let the events be
E : number 2 appears at least at least once
F : the sum of the numbers appearing is 7.
The elementary events favorable to the occurence of E are
(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2). (6, 2).
The elementary events favorable to the occurance of F are
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1).
The elementary events favorable to the occurence of both E and F are (2, 5),(5. 2).
