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March 5th, 2015, 11:37 AM  #1 
Newbie Joined: Mar 2015 From: USA Posts: 1 Thanks: 0  Probability of *not* guessing the right card in a 52card deck...
Hello. For some reason I'm having a hard time wrapping my mind around this and I can't figure out the answer. It's a question I just started wondering about. Say you have a 52card deck. You decide to try 52 times to guess the top card of the deck. After each attempt, you put the card back and shuffle the deck. What is the probability that, at the end of the 52 attempts, you guessed correctly 0 times? I know the probability of guessing the top card correctly 1 time out of those 52 attempts is, well, 1/52. But what about guessing correctly 0 times? 
March 5th, 2015, 11:56 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
The chance of guessing wrong in a particular attempt is 51/52. You do this 52 times, so the probability is (51/52)^52.  

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