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April 10th, 2017, 07:30 AM  #1 
Newbie Joined: Jan 2017 From: Britain Posts: 18 Thanks: 0  Combined events probabilityHELP!
Trying to learn probability and struggling with following two questions  any help appreciated: 1. A group of people took a literacy and numeracy test. 85% of applicants passed the literacy test and 75% of applicants passed the numeracy test. What are the maximum and minimum proportions of people who did not pass either test? 2. 100 students. 36 study French/42 study Spanish/47 Study German. 10 study both French and German 12 Study both Spanish and German 9 study both French and German What is the probability that a student chosen at random studies all three? I tried using Venn diagrams as I was instructed to, but kept getting stuck. Last edited by skipjack; April 10th, 2017 at 08:26 AM. 
April 10th, 2017, 08:23 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,232 Thanks: 1437  VennDiagrams.PNG Above are Venn diagrams for the first question. The second question is misworded. 
April 10th, 2017, 11:33 AM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 573 Thanks: 79 
I'm going to guess that the third line is supposed to say "French and Spanish." The sum of the three individual amounts is 125 and the sum of the paired amounts is 31. I don't think there's enough information. Aren't both of these possible? 1. 6 don't study any language 10 study both French and German but not Spanish 12 Study both Spanish and German and but French 9 study both French and Spanish but not German 0 study all three 17 study French only 25 study German only 21 study Spanish only 2. 9 don't study any language 7 study both French and German but not Spanish 9 study both Spanish and German and but French 6 study both French and Spanish but not German 6 study all three 17 study French only 25 study German only 21 study Spanish only There are other ways. 
April 11th, 2017, 01:25 AM  #4 
Newbie Joined: Jan 2017 From: Britain Posts: 18 Thanks: 0  Wording in UK GCSE text book
Thanks for responses, My wording for the second question is correct according to a maths book here in UK for year 11 (16 year olds). I had the same problem seems like not enough information. Thanks for venn diagrams for first question, I didn't think of how they can be 'nested' like that. 
April 11th, 2017, 01:26 AM  #5 
Newbie Joined: Jan 2017 From: Britain Posts: 18 Thanks: 0 
Sorry , just noticed wrong wording!!! Yes, French and Spanish no wonder I make so many mistakes in maths!


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