A player draws the cards from the a 52-card deck one by one, without putting them back in the deck.
Every time before drawing a card he guesses the suit of the card he will draw.
He decides to always guess the suit that occurs most frequently in the remaining deck (if there are several such suits, he chooses any one of them).

Prove that he will guess the right suit at least 13 times.

Of course it is true using the given method. We actually only need 1 card of each suit to see why. The player is then forced by the method to select at least one of the cards correctly, even if they are played face up and the player deliberately selects a 'wrong' suit whenever permitted to do so.

Accordingly, this is not strictly a demonstration of randomness. Once the method is set aside, even if we force the player to select each suit exactly 13 times, there will still be (infrequent) cases where an otherwise random selection will fail to yield a single correct guess, as is easily shown.

Posted by broll on 2015-07-22 05:26:02