A survey of 100 students produced the following statics: 32 study mathematics, 20 study physics, 45 study Biology, 15 study mathematics and biology, 7 study mathematics and physics, 10 study physics and Biology, 30 do not study any of the three subjects
1, Present the information in a Venn Diagram
ii, Find the number of students who study all the three subjects
iii, Take exactly one of the three subjects

  1. 👍
  2. 👎
  3. 👁
  1. We don't know the intersection of all three circles, so label it x
    Now go to the intersection of two of the circles, say, the M and B circles
    It says that sum is 15, but we have already counted x of them, so in the remaining part of the football-shaped region is 15-x
    Do that for the other two intersection of pairs to have 10-x and 7-x

    Now go to the whole circles, start with M
    We have already counted, 15-x, x, and 7-x
    or 22-x
    But the whole math circle contains 32, so the open part must be 32-(22-x) = 10+x
    Do the same with the other whole circles and get
    20+x and 3+x

    Now add them all up.
    We can use a short-cut here, we know that everything in the Math circle is 32, so ..

    32 + 10-x + 20+x + 3+x = 70
    x = 5

    ii) 5 take all three subjects
    ii) add up all the parts in the outer parts of the circle which do not intersect with any other circles
    that is,
    Math only = 27
    Biology only = 25
    Physics only = 8


    using the formula:
    N(M or P or B) = N(M) + N(B) + N(P) - N(M and P) - N(M and B) - N(P and B) + N(M and P and B)
    70 = 32+45+20 - 7 - 15 -10 + x
    x= 5

    1. 👍
    2. 👎
  2. Maths only is 25 because 45+5-25
    Bio only is 15 because 32+5-22
    Physics only is 8 because 20+5-17

    1. 👍
    2. 👎
  3. 屌你

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Education Tech

    1.) Which of the following is the best strategy for studying test? a) Sitting alone in a chair in a quiet room, looking over your textbook. b) Working in pairs and exchanging practice questions. c) Developing a personal method

  2. math

    A school has 63 students studying Physics, Chemistry and Biology. 33 study Physics, 25 Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study Biology and Chemistry while 8 study both Physics and Biology. Equal numbers

  3. maths

    In a class of 80 students, 53 study Art, 60 study Biology, 36 study Art and Biology, 34 study Art and Chemistry, 6 study Biology only and 18 study Biology but not Chemistry. Illustrate the information on a Venn diagram. Determine

  4. Mathematics

    in a class of 80 students,40 study physics, 48 study mathematics and 4 4 study chemistry. 20 study physics and mathematics. 24 study physics and chemistry and 32 study only two of the three subjects. if every student studies at

  1. maths

    A survey o 85 students asked them about the subjects they liked to study 35 students liked maths,37liked history,26 liked physics,20 liked maths and history,14 liked maths and physics,2 liked all the subjects. a) how many of these

  2. Math

    In a class of 40 students,the number of students who study history is 10 more than those who study French,if 8 students study both subject,then how many study French and how many study history ?

  3. Algebra

    70 students are studying mathematics,physics & chemistry.40 students study mathematics,35 study physics and 30 study chemistry.15 students are studying all the three subjects.How many students are studying exactly two of the

  4. Mathematics

    All 30 students in a class study at least 1 of the 2 subjects history or Geography .Twice as many study History as Geography .By drawing a Venn diagram or otherwise , find the number of students who study both History and

  1. language arts

    Choose the detail that would best support the following main idea for an argumentative essay. Studying on a regular basis improves grades. 1 students who study also try to eat healthier snacks 2 Students who study on a regular

  2. Mathematics

    There are 30 students in the class. 16 of them study french and 21 study spanish. They all study at least one of the two languages. What is the probability that a student chosen at random studies french only?

  3. Mathematics

    In a class of 100 students,37 study maths,32 study physics 31 study chemistry,9 study maths and physics 12 study maths and chemistry,11 study physics and chemistry,28 study none of these. Illustrate the information in a Venn

  4. St.Peter's Boys Senior High School

    In a class of 500 students,60 study geography,40 study English,30 study geography and history,25 study English and history,if 10 study all the three subjects,find using venn diagram the number of students who study none of the

You can view more similar questions or ask a new question.