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. 👍 0
  2. 👎 0
  3. 👁 427
asked by Navami
  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. 👍 1
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

    asked by Japs on February 9, 2020
  2. Mathematics

    In an examination conducted for 60 candidates,the number of candidate who passed in Maths is 15 more than those who passed science and 7 failed both subject 12 candidates passed both subject 1.Draw a Venn diagram to illustrate

    asked by Bobby Osei Kusi on January 15, 2019
  3. math

    out of 100 students in a final examination of class 10, 70 passed in mathematics, 60 passed in science and 10 failed in both subject If 10 students absent find the number of students who passed both subject by using venn diagram

    asked by pawan on July 2, 2012
  4. mathematics

    1. In an examination conducted for 80 candidates, those who passed in mathematics were 17 more than those who passed science and 9 failed both subjects.14 candidates passed both subjects. I. Draw a venn diagram to illustrate this

    asked by partey on October 30, 2011
  5. Math

    In a group of 105 students, 70 students passed Mathematics, 60 students passed History and 45 students passed Geography; 30 students passed Mathematics and History, 35 students passed History and Geography, 25 passed Mathematics

    asked by Lucas on January 24, 2014
  1. math

    In a group of 105 students, 70 students passed Mathematics, 60 students passed History and 45 students passed Geography; 30 students passed Mathematics and History, 35 students passed History and Geography, 25 passed Mathematics

    asked by Lucas on January 23, 2014
  2. Probability

    A college professor has been studying the relationship between the attendance habits of his students and the grades they earn in his courses. A breakdown of 200 of his students revealed the following: Attended regularly --- 160

    asked by Angela on May 14, 2011
  3. Math

    There are 24 students in Mrs.Smith's 1st block class. 1/4 of the class passed the math test with an A. 12 students in the class passed the math test with a B. What percent of the students in the class passed the test? ****** This

    asked by Grace on March 1, 2012
  4. ma

    In a class of 100 students, 40 failed in Math, 30 failed in Physics, 60 failed in Chemistry. 35 passed in both Math and Physics. 20 passed in Physics and Chemistry. 25 passed in Math and Chemistry. Each student passed in at least

    asked by Anonymous on September 7, 2016
  5. statistics

    In class of 125 students, 70 students passed in Math, 56 students passed in Statistics, and 30 passed in both. The probability that a student selected at random from the class, has passed in only one subject is

    asked by Anonymous on March 22, 2012

More Similar Questions