- WELCOME TO A LESSON ON SOLVING PROBLEMS USING VENN DIAGRAMS.
LET'S TAKE A LOOK AT OUR FIRST EXAMPLE.
150 COLLEGE FRESHMEN WERE INTERVIEWED.
SO THESE STUDENTS MAKE UP OUR UNIVERSAL SET FOR THIS EXAMPLE.
85 WERE REGISTERED FOR A MATH CLASS,
70 WERE REGISTERED FOR AN ENGLISH CLASS,
AND 50 WERE REGISTERED FOR BOTH A MATH AND ENGLISH CLASS.
THE SET UP THIS VENN DIAGRAM,
WE'RE GOING TO WORK OUR WAY BACKWARDS,
SO WE'LL START WITH THIS INFORMATION HERE
AND WORK OUR WAY UPWARDS.
SO 50 WERE REGISTERED FOR BOTH MATH AND ENGLISH.
THERE ARE 50 STUDENTS IN THIS REGION HERE
WHERE MATH AND ENGLISH OVERLAP.
NEXT WE'RE TOLD THAT 70 WERE REGISTERED FOR AN ENGLISH CLASS.
AND NOTICE THAT OF THESE 70, 50 OF THEM WERE ALSO TAKING MATH.
SO 70 - 50 = 20 STUDENTS TAKING ONLY ENGLISH.
SO WHEN IT SAYS 70 WERE REGISTERED FOR ENGLISH,
WE HAVE TO ALSO COUNT THOSE TAKING ENGLISH AND MATH,
OR THESE 50 HERE.
AND THEN 85 WERE REGISTERED FOR A MATH CLASS.
AGAIN, 50 OF THE 85 WERE ALREADY ACCOUNTED FOR,
LEAVING 35 THAT JUST TAKE MATH.
AND SINCE 150 STUDENTS WERE INTERVIEWED,
NOTICE THAT 35 + 50 + 20 ARE THE ONLY STUDENTS
THAT HAVE BEEN ACCOUNTED FOR SO FAR,
WHICH IS 105 STUDENTS,
WHICH MEANS THERE MUST BE 45 STUDENTS IN THIS REGION HERE
THAT ARE NOT TAKING MATH OR ENGLISH.
NOW LET'S ANSWER THE QUESTIONS.
NUMBER ONE, HOW MANY SIGNED UP ONLY FOR A MATH CLASS?
WELL, THAT WOULD BE THESE 35 STUDENTS HERE.
HOW MANY SIGNED UP ONLY FOR ENGLISH CLASS?
THAT WOULD BE 20.
HOW MANY SIGNED UP FOR MATH OR ENGLISH?
THIS QUESTION IS ASKING FOR ANY STUDENT THAT TOOK A MATH CLASS
OR AN ENGLISH CLASS.
SO IT WOULD BE ALL THE STUDENTS IN THIS ENTIRE REGION HERE.
SO 35 + 50 = 85 + 20 = 105.
AND THEN, NUMBER FOUR,
HOW MANY SIGNED UP FOR NEITHER MATH OR ENGLISH?
THAT WOULD BE THE STUDENTS OUTSIDE OF OUR CIRCLES HERE,
WHICH WOULD BE 45 STUDENTS.
NOW LET'S TAKE A LOOK AT A SECOND EXAMPLE.
AND NOTICE FOR THIS ONE
WE HAVE THREE DIFFERENT COURSES TO BE CONSIDERED.
100 STUDENTS WERE INTERVIEWED.
28 TOOK PE, 31 TOOK BIOLOGY, 42 TOOK ENGLISH,
9 TOOK PE AND BIOLOGY, 10 TOOK PE AND ENGLISH,
6 TOOK BIOLOGY AND ENGLISH, AND 4 TOOK ALL THREE SUBJECTS.
AGAIN, WE'RE GOING TO WORK OUR WAY FROM THE BOTTOM TO THE TOP
TO COMPLETE OUR VENN DIAGRAM.
SO IF 4 STUDENTS TOOK ALL THREE SUBJECTS,
ONLY REGION WHERE ALL THREE SUBJECTS OVERLAPPED
IS IN THE MIDDLE HERE,
SO THERE ARE 4 STUDENTS HERE.
NEXT, 6 TOOK BIOLOGY AND ENGLISH.
BIOLOGY AND ENGLISH OVERLAP IN THIS REGION HERE.
NOTICE THAT 4 OF THE 6 STUDENTS ARE TAKING ALL 3 SUBJECTS.
SO THAT LEAVES ONLY 2 STUDENTS HERE
THAT ARE TAKING ONLY BIOLOGY AND ENGLISH.
SO WHEN IT SAYS 6 TOOK BIOLOGY AND ENGLISH,
WE ALSO HAVE TO INCLUDE THE STUDENTS
THAT ARE TAKING ALL THREE SUBJECTS.
SO IF 10 TOOK PE AND ENGLISH,
THAT WOULD BE IN THIS REGION HERE.
AGAIN, 4 OF THE 10 ARE IN THIS REGION,
SO WE HAVE 6 TO MAKE UP A TOTAL OF 10 TAKING PE AND ENGLISH.
AND THEN 9 TOOK PE AND BIOLOGY.
SO FOR THIS REGION HERE, 4 OF THE 9 ARE ALREADY ACCOUNTED FOR,
LEAVING 5 IN THIS REGION HERE
THAT ARE TAKING ONLY PE AND BIOLOGY.
AGAIN, NOTICE 9 TOTAL ARE TAKING PE AND ENGLISH, AS STATED.
42 TOOK ENGLISH.
SO THE NUMBER OF STUDENTS IN THIS ENTIRE REGION HERE
MUST BE 42.
AGAIN, NOTICE THAT 12 HAVE ALREADY BEEN ACCOUNTED FOR,
LEAVING 30 THAT TAKE ONLY ENGLISH.
AND THEN 31 TOOK BIOLOGY.
WELL, AGAIN, NOTICE THAT THIS REGION HERE IS BIOLOGY.
5 + 4 + 2, OR 11 STUDENTS ARE ALREADY ACCOUNTED FOR,
LEAVING 20 IN THIS REGION HERE.
AND NOW WE HAVE 28 TOOK PE.
NOTICE THAT 15 ARE ALREADY ACCOUNTED FOR THAT TAKE PE,
LEAVING 13 IN THIS REGION HERE.
AND THESE 13 ONLY TAKE PE.
NOW, THE LAST STEP IS TO DETERMINE,
OF THESE 100 STUDENTS,
HOW MANY ARE NOT TAKING ANY OF THESE THREE SUBJECTS.
SO LET'S SEE HOW MANY STUDENTS HAVE BEEN ACCOUNTED FOR.
WE HAVE 30 + 20 + 13 = 63, PLUS 6 + 4 + 5 + 2 = 17,
SO 80 STUDENTS HAVE BEEN ACCOUNTED FOR OF THE 100,
LEAVING 20 MORE
THAT ARE NOT TAKING ANY OF THESE THREE SUBJECTS.
NOW THAT WE HAVE THE VENN DIAGRAM COMPLETED,
WE SHOULD BE ABLE TO ANSWER ALL THESE QUESTIONS.
HOW MANY STUDENTS TOOK NONE OF THE THREE SUBJECTS?
WELL, THAT WOULD BE 20,
THE STUDENTS THAT ARE NOT IN ANY OF THESE REGIONS HERE.
HOW MANY STUDENTS TOOK PE BUT NOT BIOLOGY OR ENGLISH?
ANOTHER WAY TO SAY THIS IS HOW MANY TOOK JUST PE,
WHICH WOULD BE THESE 13 STUDENTS.
AND THE LAST QUESTION, HOW MANY STUDENTS TOOK BIOLOGY AND PE,
BUT NOT ENGLISH?
THEY TOOK BIOLOGY AND PE, THEY'RE IN THIS REGION HERE.
BUT THESE 4 DID TAKE ENGLISH,
SO IT'S ONLY GOING TO BE 5 THAT TOOK BIOLOGY AND PE.
THAT'S GOING TO DO IT FOR THIS VIDEO.
I HOPE YOU FOUND THIS HELPFUL.