Solution Found!
An elementary school is offering 3 language classes: one
Chapter 2, Problem 12P(choose chapter or problem)
Problem 12P
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class, and 16 in the German class. There are 12 students who are in both Spanish and French, 4 who are in both Spanish and German, and 6 who are in both French and German. In addition, there are 2 students taking all 3 classes.
(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?
(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
Questions & Answers
QUESTION:
Problem 12P
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class, and 16 in the German class. There are 12 students who are in both Spanish and French, 4 who are in both Spanish and German, and 6 who are in both French and German. In addition, there are 2 students taking all 3 classes.
(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?
(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
ANSWER:
Step 1 of 4
It is given that a school is offering 3 language classes Spanish, French and German for it's all 100 students.
There are 28 students in Spanish class, 26 students in French class and 16 students in German class.
12 students take both Spanish and French classes, 4 students take both Spanish and German classes and 6 students take both French and German classes.
Also it is given that 2 students are taking all the three classes.
Using this we need to find the required values.