This is the solution using substitution. Hope this helps!
Example 1
1 answer:
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Answer:
A. 0.5
B. 0.32
C. 0.75
Step-by-step explanation:
There are
- 28 students in the Spanish class,
- 26 in the French class,
- 16 in the German class,
- 12 students that are in both Spanish and French,
- 4 that are in both Spanish and German,
- 6 that are in both French and German,
- 2 students taking all 3 classes.
So,
- 2 students taking all 3 classes,
- 6 - 2 = 4 students are in French and German, bu are not in Spanish,
- 4 - 2 = 2 students are in Spanish and German, but are not in French,
- 12 - 2 = 10 students are in Spanish and French but are not in German,
- 16 - 2 - 4 - 2 = 8 students are only in German,
- 26 - 2 - 4 - 10 = 10 students are only in French,
- 28 - 2 - 2 - 10 = 14 students are only in Spanish.
In total, there are
2 + 4 + 2 + 10 + 8 + 10 +14 = 50 students.
The classes are open to any of the 100 students in the school, so
100 - 50 = 50 students are not in any of the languages classes.
A. If a student is chosen randomly, the probability that he or she is not in any of the language classes is
B. If a student is chosen randomly, the probability that he or she is taking exactly one language class is
C. If 2 students are chosen randomly, the probability that both are not taking any language classes is
So, the probability that at least 1 is taking a language class is