Overview of Student Enrollment Data
A total of 160 students attend a language school where instruction is exclusively in Spanish or English. The students study either biology, mathematics, or both. The data is represented using a Venn diagram with three sets:
- S: Students taught in Spanish
- B: Students studying biology
- M: Students studying mathematics
Key Calculations and Findings
A. Number of Students Taught in Spanish
- Add all numbers within the Spanish set (S).
- Total students taught in Spanish = 95.
B. Number of Students Studying Mathematics in English
- Since students are taught only in Spanish or English, those studying mathematics but not in Spanish are studying in English.
- Mathematics students in English = 12 + 20 = 32.
C. Number of Students Studying Both Biology and Mathematics
- Add students in the intersection of biology and mathematics.
- Total = 12 + 40 = 52.
D. Number of Students Taught in Spanish Studying Biology or Mathematics
- Calculate the union of biology and mathematics within the Spanish set.
- Sum values in Spanish who study biology or mathematics: 10 + 40 + 28 = 78.
E. Number of Students Studying Both Biology and Mathematics but Not Taught in Spanish
- Find the intersection of biology and mathematics outside the Spanish set.
- Total = 12.
F. Probability a Student Studies Mathematics
- Total mathematics students = 100.
- Probability = 100 / 160 = 0.625 or 62.5%.
G. Probability a Student Studies Neither Biology Nor Mathematics
- Count students outside both biology and mathematics sets.
- Total = 17 + 25 = 42.
- Probability = 42 / 160 = 0.2625 or 26.25%.
H. Probability a Student is Taught in Spanish Given They Study Biology
- Use conditional probability formula: P(S|B) = P(S ∩ B) / P(B).
- Students in both Spanish and biology = 10 + 40 = 50.
- Total biology students = 70.
- Probability = 50 / 70 ≈ 0.714 or 71.4%.
Summary
This analysis demonstrates how to use Venn diagrams and set theory to interpret student enrollment data effectively. It provides actionable insights into language instruction and subject study patterns, along with probability calculations useful for educational planning and decision-making.
For a deeper understanding of the concepts used in this analysis, you may find the following resources helpful:
question six 160 students attend a du Language School in which the students are taught only in Spanish or taught
only in English a survey was conducted in order to analyze the number of students St
studying biology or mathematics the results are shown in the v
diagram set s represents those students who are taught in Spanish set B represents those students
who study biology set M represent those students who study
mathematics a find the number of students in the school that are taught in
Spanish when you are given a full vend diagram you need to figure out the number of elements in each
set for set B you need to add these four numbers together which is a
70 for mathematics you need to add the value in this
circle together which is 100 for Spanish you need to add these
four numbers together which is a 95 so for
a answer is 95 for B find the number of students in the school that study mathematics in
English based on this information students are taught only in Spanish or taught only in
English so this two group of students are
studying mathematics in English n for M intersection
E equals 12 + 20 = 32 let's go to say find the number of four students in the school that study
both biology and Mathematics I these two adding together 12 + 40 equals
52 D write down n of for S intersection M Union B because the value must be in s so
choose these four values then we will do the sub traction M Union b means either in M or in
B then you need to get rid of the values that are not in M or not in B since the 17 doesn't belong to b or M you need to
get rid of this uh 17 we need to add add this three together 10 + 40 + 28 equal 78 e write down n of B intersection M
intersection S Prime let's do B intersection M first B intersection m is this two then
not in s so the value in s you need to cross out equals
12 a student from the school is chosen at rhom F find the probability that these students study
mathematics 100 students study mathematics therefore the probability of
M = 100 over
160 G find the probability that these students studies neither biology nor mathematics neither
biology check the number outside of this biology Circle we have four numbers no mathematics
which means cross out the number in the mathematics Circle we have a two number
left 17 + 25 equals 42 so this a probability of for B Prime
intersection M Prime equals 42 over 160 let's go to H find the probability that the students is taught in
Spanish given that the students study biology we are looking for probability of
Spanish given that the students study biology eal let's use this formula so we have a
probability of for S intersection B all over probability of b equals s intersection B is this
two so 10 + 40 all over elements in set B is is a 70 so 50 over 70 is the solution
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