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April 28th, 2013, 03:16 PM  #1 
Newbie Joined: Apr 2013 Posts: 3 Thanks: 0  Can you help me figure out "at least one" probability questi
A cooler contains 11 cans of soda; 5 colas, 5 orange and 1 cherry. Two cans are selected at random without replacement. Find the probability that at least 1 can is cherry. I need stepbystep help with this one, not just an answer. I have tried many examples and have no idea what I'm doing or even how to make sense of the example. Any help is greatly appreciated. 
April 28th, 2013, 04:13 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
The chance that the first can chosen is cherry is 1/11. The chance that the first can chosen is not cherry and the second can chosen is cherry is (10/11)(1/10) = 1/11. Hence the required probability is 1/11 + 1/11 = 2/11. 
April 28th, 2013, 04:31 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Can you help me figure out "at least one" probability qu Hello, lilmscris! Here is another approach. Quote:
 
April 28th, 2013, 04:39 PM  #4  
Newbie Joined: Apr 2013 Posts: 3 Thanks: 0  Re: Quote:
 
April 28th, 2013, 04:43 PM  #5 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Can you help me figure out "at least one" probability qu
A third way: What are the chances of NOT getting a cherry in two draws? First draw, there is a 10/11 chance of not getting a cherry. Second draw, given the first draw, is 9/10 chance. (10/11)(9/10) = 9/11 chance of NOT drawing a cherry. So the chance of drawing a cherry is 1(9/11) 0r 2/11 If you understand why all these methods gave the same result, you will understand the problem very well. 
April 28th, 2013, 05:02 PM  #6  
Newbie Joined: Apr 2013 Posts: 3 Thanks: 0  Re: Can you help me figure out "at least one" probability qu Quote:
 

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