You are analyzing a large group of students who are studying different international languages at a major university specializing in linguistics. In going through the data, you observe that:

• 68% study Spanish
• 34% study Portuguese
• 48% study Japanese
• 14% study both Spanish and Portuguese
• 8% do NOT study any of the above three languages: Spanish, Portuguese, Japanese
• 15% study Spanish and French
• 6% study Spanish and Japanese
• 1% study all three languages

1. Are the events study Spanish and Portuguese independent?
2. Are the events study Spanish and Japanese independent?
3. Are the events study Spanish and study Portuguese disjoint?
4. If you pick one student at random, what is the probability that that student studies either Spanish or Portuguese?
5. What percentage of students do not study Portuguese?
6. What percentage of students do not study French?
7. What portion of students studies Portuguese but not Spanish?

Note: This may or may not be useful to you in your calculations, but just to help avoid confusion: If we say, for example, that "68% study Spanish", this does not mean that those students study only Spanish. Those students might well also be taking Italian, Mandarin, or any other language.