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  1. R

    The moviegoers' club

    Each one of the 23 members of a moviegoers' club has selected his two favorite movies from a 50 movies list. It is noted that any two members have at least one favorite movie in common. What is the largest number of members that have necessarily selected a same movie? Prove that.
  2. R

    Sister probability

    Suppose boys and girls are born at the same rate. A new family has just moved to your next door. Besides the parents, you know there are 2 adolescents, and your sister has already told you at least one of them is a boy. What is the probability that the other one is a girl?
  3. R

    Balls in boxes ( probability )

    You have 3 indistinguishable boxes, containing each one, 2 colored balls: black+black, black+white & white+white. You open one box and, whithout seeing its interior, you take one white ball. What is the probability of taking a second white ball from the same box?