SOLUTION: You are a principal in a certain school with 30 teachers. Nineteen of them are teaching English, 17 are teaching Mathematics, and 15 are teaching both subjects. The head of the com
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Question 1193358: You are a principal in a certain school with 30 teachers. Nineteen of them are teaching English, 17 are teaching Mathematics, and 15 are teaching both subjects. The head of the committee on Curriculum Instruction tasked you to determine the teaching loads of the teachers in English and Mathematics for teachers' development program. You are to submit a report that shows the following:
a. A Venn diagram to illustrate the given
b The number of teachers who teach English only and the number of teachers who teach Mathematics only.
c. The probability of choosing a teacher who
(1) teaches mathematics only
(2) teaches English only
(3) teaches both subjects
(4) teaches neither subject Answer by ikleyn(52756) (Show Source):
You can put this solution on YOUR website! .
You are a principal in a certain school with 30 teachers.
Nineteen of them are teaching English, 17 are teaching Mathematics, and 15 are teaching both subjects.
The head of the committee on Curriculum Instruction tasked you to determine the teaching loads
of the teachers in English and Mathematics for teachers' development program.
You are to submit a report that shows the following:
a. A Venn diagram to illustrate the given
b The number of teachers who teach English only and the number of teachers who teach Mathematics only.
c. The probability of choosing a teacher who
(1) teaches mathematics only
(2) teaches English only
(3) teaches both subjects
(4) teaches neither subject
~~~~~~~~~~~~~~~
You will learn much more about solving such problems, if instead
of drawing Venn diagram will apply your logic and common sense.
(1) To find the number of teachers who teach Math only,
subtract 15 (teach both subjects) from 17 (teach Math).
Thus you get 17-15 = 2 teachers teach Math only.
Then the answer to quiestion (1) is = .
(2) To find the number of teachers who teach English only,
subtract 15 (teach both subjects) from 19 (teach English).
Thus you get 19-15 = 4 teachers teach English only.
Then the answer to quiestion (2) is = .
(3) The number of those teachers who teach both subject is given: it is 15.
Therefore, the answer to the third question is = .
(4) 15 teachers teach both subjects; 2 teach Math only and 4 teach English only.
Hence, the number of those teachers who teach at least one subject is 15 + 2 + 4 = 21.
It implies that the number of teachers in the school who teaches neither of the two subjects is 30-21 = 9.
Thus the answer to the last question is = .
