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April 10th, 2017, 06:30 AM   #1
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Combined events probability-HELP!

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 07:26 AM.
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April 10th, 2017, 07:23 AM   #2
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VennDiagrams.PNG
Above are Venn diagrams for the first question. The second question is misworded.
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April 10th, 2017, 10:33 AM   #3
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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.
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April 11th, 2017, 12:25 AM   #4
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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.
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April 11th, 2017, 12:26 AM   #5
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Sorry , just noticed wrong wording!!! Yes, French and Spanish -no wonder I make so many mistakes in maths!
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