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
 👍
 👎
 👁
 ℹ️
 🚩
2 answers

If 10 failed in both, that means 13010=120 passed at least one subject.
Since 85 passed math, 60 passed science, there are 145 passes from 120 students. We conclude that 145120=25 passed both.
Hence (b) 12025=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)=1P(A∪B)
P(A)=85/130
P(B)=60/130
P'(A∪B)=1P(A∪B)=10/130
=>
P(A∪B)=(13010)/130=120/130
We also know that:
P(A∪B)=P(A)+P(B)P(A∩B)
120/130=85/130+60/130P(A∩B)
=>
P(A∩B)=85/130+60/130120/130=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=BA∩B=6025=35
(b)
A∪BA∩B=12025=95 👍
 👎
 ℹ️
 🚩
MathMate 
Set
 👍
 👎
 ℹ️
 🚩
El
Answer this Question
Related Questions

math
The stemandleaf plot shows the test scores of a science class. Use the plot to answer the question. 1.how many students scored 78? (1 point) 1 student 2 students 3 students 4 students

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.

Business Math
Lee and Fred are elementary school teachers. Fred works for a charter school in Pacific Palisades, California, where class size reduction is a goal for 2013. Lee works for a noncharter school where funds do not allow for class size reduction policies.

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

please help urgent science
In science class, a group of students were using a Bunsen burner to do a flame test on various chemicals. What safety precautions should the students follow to prevent injuries?

mathematics
in an examination,31 candidates passed chemistry,29 passed physics and 3 failed both subjects,if 50 candidates sat for examination,how many of them passed chemistry only ?

math
In a class of 60 students, on average, 8 will be lefthanded. If a class includes 12 "lefties", estimate how many students are in the class.

Mathematics
In a group of 95 students ,the ratio of students who like mathematics and science is 4:5 If 10 of them like both the subject and 15 of them like none of the subject then by drawing a veen diagram ,find how many of them (1) like only mathematics (2)like

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 this information 2.How many

Maths
Among the examinees in an examination 30%, 35% and 45% failed in Statistics, in Mathematics, and in at least one of the subjects respectively. An examinee is selected at random. Find the probabilities that a. He failed in Mathematics only b. He passed in

Further mathematics
In an examination 18 candidates passed mathematics 17 candidates passed physics 11 candidates passed mathematics and physics and 1 failed both subjects Find the number of candidates that passed mathematics only The number of candidates that passed physics

Science
If the initial amount of Carbon14 in the mammoth was 8 grams, how many halflives have passed i the fossil sample has 1 gram left? How many years have passed since the mammoth's death?

math
In a local school 34 students are enrolled in a math class, 85 are enrolled in an english class, 58 are enrolled in an art class, and 54 are enrolled in a history class. Construct a pie chart with this data. What is the central angle of the slice

Chemistry
Under identical conditions, separate samples of O2 and an unknown gas were allowed to effuse through identical membranes simultaneously. After a certain amount of time, it was found that 4.92 mL of O2 had passed through the membrane, but only 3.04 mL of of

Math
I have a bar graph that shows the number of students by major in the College of Arts and Science. Math shows 200 students History shows 300 students English shows 400 students Science shows 150 students Other shows 175 students What percent of students in

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 also completed the

History
Which of the following conclusions about the freedman's bureau is best supported by the illustration? A. It's assisted only african americans B. it employed only women C. it provided education to people of all ages** D. its students passed the literacy

Math
In an examination, 1/5 of the candidates failed. It is known that 240 candidates passed. How many candidates took the examination

Physics
100g of radioactive element X are placed in a sealed box. The halflife of this isotope of X is 2 days. After 4 days have passed, what is the mass of element X in the box? b) If the box is completely evacuated (perfect vacuum), then N atoms of X are added.

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 and Geography, and 15
Still need help?
You can ask a new question or browse existing questions.