My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum

LinkBack Thread Tools Display Modes
March 22nd, 2015, 05:34 PM   #1
Joined: Mar 2015
From: MA

Posts: 1
Thanks: 0

Probability question involving a deck of cards

Hi, I have a probability question that I was hoping someone could help me with. I was playing cards with a friend and I asked them if they could pick the 3 of hearts from the deck. They tried and were incorrect. I put that card aside and said try again so now they had a 1 in 51 chance of getting it right but they were wrong again. We did this many times about 25 cards before he got the 3 of hearts. We then had a disagreement about the probability of never picking the right card so you try 51 times and are wrong every time and the last card was the one you were trying to pick. I thought the probability of that happening was like 1 in a billion but my friend thought the odds of that happening were a lot smaller. How would one figure this math question out and does anyone know the answer. It would start with having around a 98% chance of not picking the one card and would go all the way down to the end where you had a 50% chance of picking the card you were trying to avoid. What’s the probability you never pick the chosen card? Thanks for anyone who could give some insight into the question.
cardman24 is offline  
March 22nd, 2015, 05:51 PM   #2
Senior Member
MarkFL's Avatar
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
The probability on the first draw of picking the wrong card is 51/52, and on the second draw is 50/51 and so on down to the last draw where the probability of getting the wrong card is 1/2. Thus, the probability at the start of the game of picking the wrong card 51 times is 51!/52! = 1/52.
MarkFL is offline  
March 22nd, 2015, 09:31 PM   #3
Math Team
Joined: Dec 2013
From: Colombia

Posts: 7,657
Thanks: 2635

Math Focus: Mainly analysis and algebra
This is easily seen if you make your first 51 choices before looking at any of the cards. You have picked all but 1 of the 52 cards. This is therefore equivalent to picking 1 card that you won't choose.
v8archie is offline  
March 23rd, 2015, 10:02 AM   #4
Math Team
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Hello, cardman24!

The problem reduces to this question:
What is the probability that the Three of Hearts is the last card?

There are 52 choices for the last card.
There is only one Three of Hearts.

soroban is offline  

  My Math Forum > High School Math Forum > Probability and Statistics

cards, deck, involving, probability, question

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
A deck of cards pedro malafaya Elementary Math 3 May 27th, 2013 07:56 AM
Probability with Deck of Cards flyingL123 Advanced Statistics 1 October 16th, 2011 10:05 PM
Deck of Cards Probability carolinegustin Probability and Statistics 3 March 27th, 2011 07:28 PM
Fair deck of 52 Cards wowbringer Algebra 1 March 17th, 2011 09:05 PM
Possibilities with a standard deck of cards? Krimi Algebra 3 January 19th, 2008 07:52 PM

Copyright © 2019 My Math Forum. All rights reserved.