A college is offering three language classes: Spanish, French, and Japanese. These classes are open to any of the 100 students in the college. Currently, there are 28 students enrolled in the Spanish class, 26 in the French class, and 16 in the Japanese class. Among these students, 12 are enrolled in both Spanish and French, 4 in both French and Japanese, and 6 in both Spanish and Japanese. Additionally, 2 students are enrolled in all three classes. 1. If a student is chosen randomly, what is the probability that the student is taking exactly one language class? 2. If a student is chosen randomly, what is the probability that the student is not in any of these classes? 3. If two students are chosen randomly, what is the probability that at least one is taking a language class? 4. If a student is chosen randomly and it is established that he is taking at least one language class, what is the probability that the student is taking exactly two language classes?
A college is offering three language classes: Spanish, French, and Japanese. These classes are open to any of the 100 students in the college. Currently, there are 28 students enrolled in the Spanish class, 26 in the French class, and 16 in the Japanese class. Among these students, 12 are enrolled in both Spanish and French, 4 in both French and Japanese, and 6 in both Spanish and Japanese. Additionally, 2 students are enrolled in all three classes. 1. If a student is chosen randomly, what is the probability that the student is taking exactly one language class? 2. If a student is chosen randomly, what is the probability that the student is not in any of these classes? 3. If two students are chosen randomly, what is the probability that at least one is taking a language class? 4. If a student is chosen randomly and it is established that he is taking at least one language class, what is the probability that the student is taking exactly two language classes?
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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Transcribed Image Text:A college is offering three language classes: Spanish, French, and Japanese. These classes
are open to any of the 100 students in the college. Currently, there are 28 students enrolled
in the Spanish class, 26 in the French class, and 16 in the Japanese class. Among these
students, 12 are enrolled in both Spanish and French, 4 in both French and Japanese, and 6
in both Spanish and Japanese. Additionally, 2 students are enrolled in all three classes.
1. If a student is chosen randomly, what is the probability that the student is taking
exactly one language class?
2. If a student is chosen randomly, what is the probability that the student is not in any
of these classes?
3. If two students are chosen randomly, what is the probability that at least one is taking
a language class?
4. If a student is chosen randomly and it is established that he is taking at least one
language class, what is the probability that the student is taking exactly two language
classes?
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VIEWStep 2: Calculate the probability that the student is taking exactly one language class
VIEWStep 3: Calculate the probability that the student is not in any of the classes
VIEWStep 4: Calculate the probability that at least 1 is taking a language class if 2 are chosen randomly
VIEWStep 5: Calculate the probability that a student is taking exact 2 classes if he is taking at least 1 class
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