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July 23rd, 2012, 04:25 AM  #1 
Senior Member Joined: Jan 2012 Posts: 556 Thanks: 3  The Probability That Exactly One Of The Four Balls Is White
A bag contains 12 white balls and 8 black balls; another contains 10 white balls and 15 black balls. If two balls are drawn, without replacemement, from each bag, find the probability that exactly one of the four balls is white. I need working and explanation please 
July 23rd, 2012, 08:58 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,139 Thanks: 316  Re: The Probability That Exactly One Of The Four Balls Is Wh Hello, Chikis! Quote:
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July 23rd, 2012, 02:40 PM  #3 
Senior Member Joined: Jan 2012 Posts: 556 Thanks: 3  Re: The Probability That Exactly One Of The Four Balls Is Wh
Don't be offended please, I cannot see the working clearly.

July 23rd, 2012, 05:31 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 4,010 Thanks: 213  Re: The Probability That Exactly One Of The Four Balls Is Wh
1:12W,8B ; 2:10W,15B The White can be drawn 1st, 2nd, 3rd or 4th : so 4 different cases : Case1: W=12/20, B=8/19, B=15/25, B=14/24: 12/20 * 8/19 * 15/25 * 14/24 = 42/475 Case2: B=8/20, W=12/19, B=15/25, B=14/24: 8/20 * 12/19 * 15/25 * 14/24 = 42/475 Case3: B=8/20, B=7/19, W=10/25, B=15/24: 8/20 * 7/19 * 10/25 * 15/24 = 7/190 Case4: B=8/20, B=7/19, B=15/25, W=10/24: 8/20 * 7/19 * 15/25 * 10/24 = 7/190 42/475 + 42/475 + 7/190 + 7/190 = 119/475 (as per Sir Soroban!) 
July 24th, 2012, 09:53 PM  #5 
Senior Member Joined: Jan 2012 Posts: 556 Thanks: 3  Re: The Probability That Exactly One Of The Four Balls Is Wh
My thanks goes to soroban and Denis, for having intrest in my question, let me work with what you have given me. I will post more replies into the thread, if I found anything confusing with the working.

July 25th, 2012, 03:13 AM  #6 
Joined: Jul 2012 From: India Posts: 8 Thanks: 0  Re: The Probability That Exactly One Of The Four Balls Is Wh
Bag I = 12w , 8B balls Bag II = 10w , 15B balls we have 4 possibilities(Condition ) 1) Bag I(WB) and BagII(BB) = 12/20 * 8/19 * 15/25 * 14/24 2) Bag I(BW) and BagII(BB) = 8/20 * 12/19 * 15/25 * 14/24 3) Bag I(BB) and BagII(WB) = 8/20 * 7/19 * 10/25 * 15/24 4) Bag I(BB) and BagII(BW) = 8/20 * 7/19 * 15/25 * 10/24 Then P(Probability of getting exactly one white) = Condition 1 + Condition 2 + Condition 3 + Condition 4 
July 25th, 2012, 07:43 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 4,010 Thanks: 213  Re: The Probability That Exactly One Of The Four Balls Is Wh
Don't confuse the OP; that solution is exactly same as the one I gave...

August 21st, 2012, 01:53 PM  #8 
Senior Member Joined: Jan 2012 Posts: 556 Thanks: 3  Re: The Probability That Exactly One Of The Four Balls Is Wh
Thanks for the wonderful replies!

October 5th, 2012, 09:03 AM  #9 
Senior Member Joined: Jan 2012 Posts: 556 Thanks: 3  Re: The Probability That Exactly One Of The Four Balls Is Wh
What about this working: If am to choose based on logical order, I assume that the two balls are removed simultanously from each of the two bags, so they are not mutually exclusive events. FIRST BAG total number of balls in the first bag = 12+8 = 20 total number of white balls = 12 white total number of black balls = 8 probability of picking a white ball P(w) = 12/20 = 3/5 probability of picking a black ball P(b) = 8/20 = 2/5 SECOND BAG total number of balls in the second bag = 10+15 = 25 total number of white balls = 10 total number of black balls = 5 probability of picking a white ball P(w) = 10/25 = 2/5 probability of picking a black ball P(b) = 15/25 = 3/5 Bag 1 Bag 2  bw  bw  wb  wb  ww  ww  ww  ww  > 2/5*3/4*3/5*2/4 = 36/400 > 3/5*2/4*2/5*3/4 = 36/400 > = 3/5*2/4*2/5*1/4 = 12/400 > = 3/5*2/4*2/5*1/4 = 12/400 = (36+36+12+12)/400 = 96/400 = 6/25 = 0.24 That is my own working. What is your view about the working? 
October 8th, 2012, 01:00 AM  #10 
Joined: Oct 2012 Posts: 1 Thanks: 0  Re: The Probability That Exactly One Of The Four Balls Is Wh
An urn contains 8 white, 6 blue, and 9 red balls. How many ways can 6 balls be selected to meet each conditon? a) all balls are red b) 3 are blue, 2 are white, and 1 is red c) 2 are blue and 4 are red d) exactly 4 balls are white There are 8 + 6 + 9 = 23 balls total. For the first question I tried (9/23)*(8/22)*(7/21)*(6/20)*(5/19)*(4/1 but I think I did it wrong because it didn't really work out. Please help meI don't understand this! 

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