A cohort of students in a linguistics program speak a variety of languages. Following a survey, it is noted that: 68% speak Spanish 53% speak French 42% speak Mandarin 39% speak Spanish and French 22% speak Spanish and Mandarin 15% speak French and Mandarin 4% speak all three languages Answer the following: Are the events speak Spanish and speak French disjoint? Are the events speak Spanish and speak French independent? What percentage of students can not speak French?

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A cohort of students in a linguistics program speak a variety of languages. Following a survey, it is noted that:

  • 68% speak Spanish
  • 53% speak French
  • 42% speak Mandarin
  • 39% speak Spanish and French
  • 22% speak Spanish and Mandarin
  • 15% speak French and Mandarin
  • 4% speak all three languages

Answer the following:

  1. Are the events speak Spanish and speak French disjoint?
  2. Are the events speak Spanish and speak French independent?
  3. What percentage of students can not speak French? 
  4. What percentage of students knows either Spanish or Mandarin?
  5. What portion of students does not know either French or Spanish?
  6. What portion of programmers knows Spanish but not French? Hint: This is not a complicated calculation. Hint #2: If you happen to be familiar with Venn diagrams, this is a great place to use one
Expert Solution
Step 1

Given that A cohort of students in a linguistics program speak a variety of languages. Following a survey, it is noted that:

 

68% speak Spanish

53% speak French

42% speak Mandarin

39% speak Spanish and French

22% speak Spanish and Mandarin

15% speak French and Mandarin

4% speak all three languages

Using this information we have to calculate the indicated probabilities. 

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