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.

(In reply to senseless task ! by Dan Rosen)

Dan,

Your remark is correct, but irrelevant.
No one claimed the man was clever; - the question is: by acting as he did, is it possible to hit less than 13 times?
Or as Charlie surmised - and did not prove - is his method better than " spade,spade,spade,...", even when no spades are left.

Now, how about solving the puzzle ?

Bonus I:  (special for you) What is the expected number of correct guesses?

Bonus II:   Any suggestion for maximizing the result by a better strategy?

Edited on July 20, 2015, 12:37 pm

Posted by Ady TZIDON on 2015-07-20 12:33:31