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Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
  • a)
    60%
  • b)
    50%
  • c)
    25%
  • d)
    15%
  • e)
    10%
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Walking across campus, a student interviewed a group of students. 25% ...
There are two common ways of solving this problem. One involves algebra and the other involves statistical formulas.
Method 1: Use Algebra
Assign variables to the groups of interest:
Let b = the percent of students who took both classes (what we are interested in).
Let f = the percent of students who only took a finance class.
Let m = the percent of students who only took a marketing class.
We know that 40% of the students did not take either class, so 60% (=100% - 40%) must have taken either a finance class, a marketing class, or both.
This 60% is made up of those three distinct groups: those who took a finance class only, those who took a marketing class only, and those who took both:
m+f+b=60%.
We know that 25% of the students took a finance class, which is made up of those who only took this class and those who took both classes:
f+b=25%.
Likewise, 50% of the students took a marketing class, made up of those who only took marketing and those who took both:
m+b=50%.
We are interested in finding the value of b (percent who took both classes). So solve these last two equations for f and m by subtracting b from both sides of each equation:
f=25%-b.
m=50%-b.
Now plug these values of f and m into the first equation:
m+f+b=60%
50%-b + 25%-b + b = 60%.
Combine like terms to simplify:
75% - b = 60%.
Add b to both sides:
75%= 60% + b.
Subtract 60% from both sides:
15%= b.
Thus the correct answer is D.
Method 2: Use Statistical Formulas
In general, the probability of event M or F occurring is P(M∪F) = P(M) + P(F) - P(M∩F) where P(M∩F) is the probability of M and F simultaneously occurring.
In this problem:
P(M) = the probability of a student taking marketing
P(F) = the probability of a student taking finance
P(M∪F) = the probability of a student taking marketing or finance
P(M∩F) = the probability of a student taking marketing and finance; this is the variable we are trying to solve for
Fill in what we know:
P(M) = 50%
P(F) = 25%
An important insight into this problem is to realize that (the probability of a student taking marketing or finance) + (the probability of a student taking neither marketing nor finance) = 1 since these two events are complementary and complementary events must sum to one.
The question tells us that "40% took neither a finance nor a marketing class last semester." As a result, we know that 40% + P(M∪F) = 100%
Consequently: (M∪F) = 60%
Filling all that we know into the fundamental equation:
P(M∪F) = P(M) + P(F) - P(M∩F)
60% = 50% + 25% - P(M∩F)
-15% = - P(M∩F)
P(M∩F) = 15%
Thus the correct answer is D.
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Most Upvoted Answer
Walking across campus, a student interviewed a group of students. 25% ...
There are two common ways of solving this problem. One involves algebra and the other involves statistical formulas.
Method 1: Use Algebra
Assign variables to the groups of interest:
Let b = the percent of students who took both classes (what we are interested in).
Let f = the percent of students who only took a finance class.
Let m = the percent of students who only took a marketing class.
We know that 40% of the students did not take either class, so 60% (=100% - 40%) must have taken either a finance class, a marketing class, or both.
This 60% is made up of those three distinct groups: those who took a finance class only, those who took a marketing class only, and those who took both:
m+f+b=60%.
We know that 25% of the students took a finance class, which is made up of those who only took this class and those who took both classes:
f+b=25%.
Likewise, 50% of the students took a marketing class, made up of those who only took marketing and those who took both:
m+b=50%.
We are interested in finding the value of b (percent who took both classes). So solve these last two equations for f and m by subtracting b from both sides of each equation:
f=25%-b.
m=50%-b.
Now plug these values of f and m into the first equation:
m+f+b=60%
50%-b + 25%-b + b = 60%.
Combine like terms to simplify:
75% - b = 60%.
Add b to both sides:
75%= 60% + b.
Subtract 60% from both sides:
15%= b.
Thus the correct answer is D.
Method 2: Use Statistical Formulas
In general, the probability of event M or F occurring is P(M∪F) = P(M) + P(F) - P(M∩F) where P(M∩F) is the probability of M and F simultaneously occurring.
In this problem:
P(M) = the probability of a student taking marketing
P(F) = the probability of a student taking finance
P(M∪F) = the probability of a student taking marketing or finance
P(M∩F) = the probability of a student taking marketing and finance; this is the variable we are trying to solve for
Fill in what we know:
P(M) = 50%
P(F) = 25%
An important insight into this problem is to realize that (the probability of a student taking marketing or finance) + (the probability of a student taking neither marketing nor finance) = 1 since these two events are complementary and complementary events must sum to one.
The question tells us that "40% took neither a finance nor a marketing class last semester." As a result, we know that 40% + P(M∪F) = 100%
Consequently: (M∪F) = 60%
Filling all that we know into the fundamental equation:
P(M∪F) = P(M) + P(F) - P(M∩F)
60% = 50% + 25% - P(M∩F)
-15% = - P(M∩F)
P(M∩F) = 15%
Thus the correct answer is D.
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Community Answer
Walking across campus, a student interviewed a group of students. 25% ...
Given Information:
- 25% of students took a finance class last semester
- 50% of students took a marketing class last semester
- 40% of students took neither a finance nor a marketing class last semester

To Find:
- Percent of students who took both a finance and a marketing class last semester

Solution:

Step 1: Calculate the total percentage of students who took either a finance or a marketing class:
- Let F be the percentage of students who took a finance class
- Let M be the percentage of students who took a marketing class
- Let N be the percentage of students who took neither a finance nor a marketing class
F + M - (F ∩ M) + N = 100
25% + 50% - (F ∩ M) + 40% = 100
75% - (F ∩ M) + 40% = 100
35% - (F ∩ M) = 100

Step 2: Find the percentage of students who took both a finance and a marketing class:
- Let x be the percentage of students who took both a finance and a marketing class
25% + 50% - x + 40% = 100
75% - x + 40% = 100
35% - x = 100
x = 35% - 100
x = 15%
Therefore, 15% of the students in the group took both a finance and a marketing class. Hence, the correct answer is option 'D' - 15%.
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Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?a)60%b)50%c)25%d)15%e)10%Correct answer is option 'D'. Can you explain this answer?
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