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.
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?
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?