120 people are given a survey about which television shows they watch.
ABC=55
NBC=30
CBS=40
ABC and CBS=10
ABC and NBC=12
NBC and CBS and ABC=5
It wants you to solve for the remaining regions of the circle (mainly what NBC+CBS equal). I know you have to make a venn diagram but I am having issues figuring out how to solve this.
To solve this problem and find the number of people who watch both NBC and CBS, we can use the principle of inclusion-exclusion and set up an equation using the given information.
Let's define our variables:
A = Number of people who watch ABC
B = Number of people who watch NBC
C = Number of people who watch CBS
X = Number of people who watch ABC and NBC
Y = Number of people who watch ABC and CBS
Z = Number of people who watch ABC, NBC, and CBS
Based on the information given, we have:
A = 55
B = 30
C = 40
X = 12
Y = 10
Z = 5
Now, let's use the principle of inclusion-exclusion which states that:
(A union B union C) = (A + B + C) - (A intersection B) - (A intersection C) - (B intersection C) + (A intersection B intersection C)
We'll substitute the known values into this equation:
120 = (55 + 30 + 40) - X - Y - Z + (A intersection B intersection C)
Now, we can solve for (A intersection B intersection C):
120 = 125 - 12 - 10 - 5 + (A intersection B intersection C)
120 = 98 + (A intersection B intersection C)
(A intersection B intersection C) = 120 - 98
(A intersection B intersection C) = 22
Therefore, the number of people who watch ABC, NBC, and CBS is 22.
To find the number of people who watch both NBC and CBS, we can use the equation: (B intersection C) = X - (A intersection B intersection C)
(B intersection C) = 12 - 22
(B intersection C) = -10
The result is negative, which means there might be an error or inconsistency in the given data. Ideally, the number of people who watch both NBC and CBS should be a positive value. Please double-check the provided values and ensure they are correct.