My Math Forum Fair deck of 52 Cards

 Algebra Pre-Algebra and Basic Algebra Math Forum

 March 17th, 2011, 12:29 PM #1 Newbie   Joined: Nov 2010 Posts: 9 Thanks: 0 Fair deck of 52 Cards Arrangement of 5. (5 cards are dealt out of a 52 card deck) # of arrangements: 52! / (52-5)! 5! = 2, 598, 960 Correct? Order does not matter. Random. Dependent. I need to know the probability of getting exactly no Jacks, 1 Jack, 2 Jacks, 3 Jacks, 4 Jacks --- In the 5 cards that are dealt to us. We do not know any card before knowing the next one. They are all revealed at once.
 March 17th, 2011, 09:05 PM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Fair deck of 52 Cards The key to this is that the C(52,5) = 2598960 possible hands are all equally likely. Therefore, all you have to do is to find the number of ways to choose the cards in question, and divide by 2598960. No jacks How many arrangements are there without jacks? Suppose you were to take the jacks out of the pack of 52, and then deal. There are 48 cards left, and C(48,5) possible hands. Therefore the probability this would happen if the jacks had stayed in the pack is C(48,5)/C(52,5). One jack Again, separate the jacks from the rest of the cards. You select one jack from the pile of 4, and then four cards from the pile of 48. There are C(4,1)*C(48,4) ways you could do this, so the probability is C(4,1)*C(48,4) / C(52,5). Two jacks Separate the jacks, then select two jacks from the pile of 4, and three cards from the pile of 48. There are C(4,2)*C(48,3) ways... etc, etc. Finally, check your answer by adding the five different probabilities. They should sum to 1.

 Tags cards, deck, fair

,

### what is a fair deck of cards

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post pedro malafaya Elementary Math 3 May 27th, 2013 07:56 AM flyingL123 Advanced Statistics 1 October 16th, 2011 10:05 PM carolinegustin Probability and Statistics 3 March 27th, 2011 07:28 PM Markgm Art 5 December 28th, 2010 07:59 AM Krimi Algebra 3 January 19th, 2008 07:52 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top