venn diagram

IN A CLASS OF 130 STUDENTS.85 PASSED IN MATHS, 60 PASSED IN SCIENCE, 10 FAILED IN BOTH.
a) how many passed in science but failed in math
b)how many failed in exactly one subject

  1. 👍
  2. 👎
  3. 👁
  1. If 10 failed in both, that means 130-10=120 passed at least one subject.

    Since 85 passed math, 60 passed science, there are 145 passes from 120 students. We conclude that 145-120=25 passed both.
    Hence (b) 120-25=95 passed (or failed) exactly one subject.

    For (a), 60 passed science, and 25 passed both, so 35 passed science but did not make math.

    A more mathematical treatment would be:
    P'(A∪B)=1-P(A∪B)
    P(A)=85/130
    P(B)=60/130
    P'(A∪B)=1-P(A∪B)=10/130
    =>
    P(A∪B)=(130-10)/130=120/130

    We also know that:
    P(A∪B)=P(A)+P(B)-P(A∩B)
    120/130=85/130+60/130-P(A∩B)
    =>
    P(A∩B)=85/130+60/130-120/130=25/130
    The cardinality of a set is the number of members in the set.
    For example, the cardinality of A is denoted by |A|, which is equal to the number of students who passed math=85.
    Hence |B|=60, |A∩B|=25, |A∪B|=120.
    (a)
    |A'∩B|=|B|-|A∩B|=60-25=35
    (b)
    |A∪B|-|A∩B|=120-25=95

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    In a class of 150 students 70 passed in verbal and 90 passed in aptitude.10 failed in both the subject.how many students passed in both subject

  2. Maths

    In an examination,60 candidates passed science or maths.if 15 passed both subjects and 9 more passed maths than science, find the number of people who passed maths and science, probability that a candidate passed exactly one

  3. Mathematics

    In a math class with 28 students, a test was given the same day that an assignment was due. There were 20 students who passed the test and 19 students who completed the assignment. There were 16 students who passed the test and

  4. Further maths

    In an examination 31 candidate passed Chemistry,29 passed Physics 3 failed both subjects.lf 50 candidates sat for the examination how many of them passed Chemistry only.

  1. maths-urgently needed

    90% of all students passed in Hindi, 85% in Maths and 150 students passed in both. calculate total number of students in the school.

  2. maths

    In a class of 60 students,the number of students who passed biology is 6 more than the number who passed chemistry.Every student passed at least one of the two subjects and 8 students passed both subjects.How many students passed

  3. statistics

    in a batch of 15 students failed in a test. the marks of 10 who have passed were 9,6,7,8,8,9,6,5,4,7.find the median of all 15 students.

  4. ashford

    Mrs. Orlof teaches two history classes, one in the morning and one in the afternoon. Yesterday she gave the same test to both classes. Anyone who failed the test must take a retest. Since a greater percentage of students who took

  1. geometry

    In a math class with 20 students, a test was given the same day that an assignment was due. There were 11 students who passed the test and 15 students who completed the assignment. There were 9 students who passed the test and

  2. Mathematics

    In an examination 60 candidates passed intergrated science or mathematics if 15 passed both subjects and 9 more passed mathematics than science 1:find the number of candidates who passed in each subjects 2: the probability that a

  3. math

    70% of Ms. Miller's class passed the test on the first try. Those who failed were able to retake and half of those students passed on their second try. If there are 20 students in the class, what overall percentage passed the

  4. Math

    In a class of 156 students who took maths and physics they all passed at leat 1 subject 75 pass math and physics.if twice has passed physics find how many students pass math only. Represent in Venn diagram.

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