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MathNet 1998 — Part 01 Question 62

Math Olympiad Vault · MathNet 1998 — Part 01

Question 62

Alberto wants to organize a poker game this evening.
He knows that Bruno and Barbara go to the gym together one evening out of three, and that Carla, Corrado, Dario and Davide are busy one evening out of two (but not necessarily on the same days).
Furthermore, he knows that Dario doesn't want to play with Davide since he took the girl away from him.
Since at least four people (including Alberto) are needed to play poker, what is the probability that there will be a game tonight?