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July 14th, 2011, 12:35 PM  #1 
Member Joined: Mar 2011 Posts: 42 Thanks: 0  Probability. A deck of card
A deck of card is shuffled. What is the chance that the top card is not the jack of clubs or the bottom card is the queen of spades? Thank you ! 
July 14th, 2011, 01:13 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,834 Thanks: 733  Re: Probability. A deck of card
Set up two disjoint events and sum probabilities. Event 1, top card is not jack of clubs  prob = 51/52 Event 2, top card is jack of clubs and bottom card is queen of spades  prob = (1/52)(1/51) Add together. 
July 14th, 2011, 01:15 PM  #3 
Newbie Joined: Jul 2011 Posts: 12 Thanks: 0  Re: Probability. A deck of card
When you have an or statement like that, there are three possibilities: 1) The top card is not the jack of clubs AND the bottom card is the queen of spades 2) The top card is not the jack of clubs and the bottom card is not the queen of spades 3) The top card is the jack of clubs and the bottom card is the queen of spades. This is a lot of probabilities to keep track of, so one way to do it is to find the probability that the or statement is NOT true and subtract that from 1. The statement is not true when the top card is the jack of clubs and the bottom card is not the queen of spades. 
July 14th, 2011, 01:15 PM  #4 
Newbie Joined: Jul 2011 Posts: 12 Thanks: 0  Re: Probability. A deck of card
The other way works too.

July 14th, 2011, 02:26 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Probability. A deck of card
P(j, q) = (1/52)*(1/52) P(nj, q) = (51/52)*(1/52) P(j, nq) = (1/52)*(51/52) P(nj, nq) = (51/52)*(51/52) P(j, q) + P(nj, q) + P(j, nq) + P(nj, nq) = 1. P(j, q) + P(nj, q) + P(nj, nq) = 2653/2704. 
July 14th, 2011, 08:04 PM  #6  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Probability. A deck of card Hello, hunnybee! Quote:
Let = Top,[color=beige] .[/color] = Bottom. Formula: [color=beige]. . . . . . . . . . . . . . . . . . [/color] [color=beige]. . . . . . . . . . . . . . . . . . [/color] edit: corrected silly error [color=beige] .[/color]  
July 15th, 2011, 02:58 PM  #7  
Global Moderator Joined: May 2007 Posts: 6,834 Thanks: 733  Re: Probability. A deck of card Quote:
 
July 15th, 2011, 03:37 PM  #8  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Probability. A deck of card Quote:
 
July 16th, 2011, 03:54 PM  #9  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Probability. A deck of card Quote:
I guess this is wrong, but can anyone tell me why?  
July 17th, 2011, 01:00 PM  #10  
Global Moderator Joined: May 2007 Posts: 6,834 Thanks: 733  Re: Probability. A deck of card Quote:
Note to soroban: The last term should be (51/52)(1/51)  

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