Brain Teaser: boy or girl?

Q: I met a man with two children and I know one of them is a boy.
   What is the probability that the other children is also a boy?

   If I know one boy's birthday is Tuesday,
   what is the probability that the other children is also a boy?

   아이가 둘인 사람을 만났는데, 그 중 적어도 한명은 남자라는 것을 안다고 하자.
   이 때, 다른 아이도 남자아이일 확률은?
   만약, 남자애가 화요일에 태어났다는 것을 안다면, 다른 아이가 남자아이일 확률은?




A: The answer is 1/3.
    One may think it is 1/2 because the the other would be either boy or a girl.
    Let us say the first child A and second child B. Then all possible situation are

    (A,B)=(boy,boy), (boy, girl), (girl, boy) and (girl,girl).

    Let us assume they are equally probable.
    From the information, we exclude (girl,girl) case.
    Then, the probability of (boy,boy) is a 1/3.

    It is tricky. If we had known that the 'first' child is a boy,
    we had only (boy,boy), (boy, girl) and the probability of the other is a boy
    becomes 1/2, consistent with naive guess.
 
    The second problem is more strange.
    In second question, the possible combinations are
    (boy-Tuesday, boy-Tuesday)
    (boy-Tuesday, boy-other 6 day)
    (boy-other 6 day, boy-Tuesday)
    (boy-Tuesday, girl-7 days)
    (girl-7 days, boy-Tuesday)
    Thus, the probability of being two-boys are (1+6+6)/(1+6+6+7+7)=13/27.
    The probability increased slightly because of additional information.

    This may sound strange because the knowledge of birthday of a boy affects the
    gender of the other?
    Let us check consistency. If we had no knowledge on the birth day. Then,
    combination becomes
    (boy-7 day, boy-7 day)
    (boy-7 day, girl-7day)
    (girl-7 day, boy-7day)
    Thus probability is (7*7)/(7*7+7*7+7*7)=1/3. It is consistent with the 1st case.