All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Probability test (Posted on 2005-03-03) Difficulty: 2 of 5
Five cards are drawn from a pack of 52 cards. What is the probability that exactly three of them are of the same suit.

See The Solution Submitted by Sandeep    
Rating: 3.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution + | Comment 3 of 12 |

Start with the probibility that the first three cards are hearts and the other two are not. That's (13/52)*(12/51)*(11/50)*(39/49)*(38/48). But this must be multiplied by C(5,3) as any three, not just the first three, could be the hearts.  Then it must be multiplied by 4, as it could be any suit, not just hearts.

It all comes out to  2717/8330 = approx. 0.3261704681872749076.

For curiosity's sake, The probability of exactly four cards being of the same suit is

(13/52)*(12/51)*(11/50)*(10/49)*(39/48)*4*C(5,4) = 143/3332 = 0.0429171668667466981

and five as

33/16660 = 0.0019807923169267705.


  Posted by Charlie on 2005-03-03 14:50:05
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information