In a survey of 300 individual investors regarding subscription to the NYT, WSJ, and UST....:

122 sub to NYT
150 sub to WSJ
62 sub to UST
38 sub to NYT and WSJ
20 sub to NYT and UST
28 sub to WSJ and UST

b) How many individual investors surveys subscribe to only one of the investors?
I just added the outermost parts of my venn diagrams (68+84+14) for 162.

c) How many investors subscribe to only one newspaper?
I am confused. Is this the same as part b???

You are not accounting for people subscribing to all 3

which would be included in the double intersection values of 38, 20, and 28

n(N or W or U) = n(W) + n(N) + n(U) - n(W and N) - n(W and U) - n(N and U) + n(W and N and U)
300 = 150+122+62 - 38 - 28 - 20 + n(W and N and U)
52 = n(W and N and U)

So 52 take all 3 papers
but n(W and N and U) ≤ 20 , or else the intersection of two at a time are negative.

so I think your data is inconsistent

Yes, part c is asking the same question as part b. Both questions are asking for the number of individual investors who subscribe to only one newspaper. In other words, it refers to the individuals who subscribe to one newspaper only and not to any of the other newspapers surveyed.

To find the number of individuals who subscribe to only one newspaper, you need to subtract the number of individuals who subscribe to multiple newspapers from the total number of individuals who subscribe to each newspaper.

In this case, you are given the following information:

- 122 individuals subscribe to the NYT.
- 150 individuals subscribe to the WSJ.
- 62 individuals subscribe to the UST.

To find the number of individuals who subscribe to only one newspaper, you can use the principle of inclusion-exclusion.

Let's assume:
- n(NYT) = number of individuals who subscribe to the NYT
- n(WSJ) = number of individuals who subscribe to the WSJ
- n(UST) = number of individuals who subscribe to the UST

We can write the equation:
Total = n(NYT) + n(WSJ) + n(UST) - (n(NYT and WSJ) + n(NYT and UST) + n(WSJ and UST)) + n(NYT and WSJ and UST)

Substituting the given values:
Total = 122 + 150 + 62 - 38 - 20 - 28 + n(NYT and WSJ and UST)

We are not given the value of n(NYT and WSJ and UST), but we can still find the number of individuals who subscribe to only one newspaper by calculating the total number of subscribers and subtracting the number of individuals who subscribe to multiple newspapers.

So, we can rewrite the equation as:
Total - (n(NYT and WSJ) + n(NYT and UST) + n(WSJ and UST)) + n(NYT and WSJ and UST) = Number of individuals who subscribe to only one newspaper

Plugging in the given values:
300 - (38 + 20 + 28) + n(NYT and WSJ and UST) = Number of individuals who subscribe to only one newspaper

Simplifying:
300 - 86 + n(NYT and WSJ and UST) = Number of individuals who subscribe to only one newspaper

Now, we know that the total number of individuals who subscribe to only one newspaper is 162, so we can solve for n(NYT and WSJ and UST):

162 = 300 - 86 + n(NYT and WSJ and UST)

Rearranging the equation:
n(NYT and WSJ and UST) = 162 - 214
n(NYT and WSJ and UST) = -52

Since the number of individuals cannot be negative, it means that there is an error in the given information or calculation.

Therefore, it is not possible to determine the exact number of investors who subscribe to only one newspaper with the given information.