My Math Forum Probability with Deck of Cards

 October 16th, 2011, 05:09 PM #1 Newbie   Joined: Oct 2011 Posts: 1 Thanks: 0 Probability with Deck of Cards I was playing a card came last night that involves a group of people picking from a deck of cards spread out across the table. After a card is picked, it is not replaced. The very last card picked in the game was a King, and the game is actually called King's, so that led to a discussion/argument over what the chances of that happening are. The question is, what are the chances that the last card picked from a deck of cards is a King. I believe I have the correct answer now, but I was very curious to post this on the forum and just see what people say and how they reason through it. I'm looking forward to hearing back! Thank you!
October 16th, 2011, 10:05 PM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

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Re: Probability with Deck of Cards

Hello, flyingL123!

You are probably making the problem harder than it is.

Quote:
 I was playing a card came last night that involves a group of people picking from a deck of cards spread out across the table.[color=beige] .[/color]After a card is picked, it is not replaced. The very last card picked in the game was a King, and the game is actually called King's, so that led to a discussion/argument over what the chances of that happening are. The question is: what are the chances that the last card picked from a deck of cards is a King?

$\text{The probability that the last card is a King is: }\:\frac{4}{52} \,=\,\frac{1}{13}$

You are probably wondering "How do we know which card is the last card?"
[color=beige]. . [/color]It doesn't matter!

Spread the entire deck face down on the table.
Point to any card and ask "What is the probabiity that it is a King?"
[color=beige]. . [/color]The answer is the same: one-thirteenth.

 Tags cards, deck, probability

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